Here we'll cover creation of a custom fluid. If you plan to create several fluids, it is recommended to make an abstract basic fluid class where you'll set necessary defaults that will be shared in its subclasses. We'll also make it generate in the world like lakes.

Vanilla fluids extend net.minecraft.fluid.FlowableFluid, and so shall we.

public abstract class TutorialFluid extends FlowableFluid {
	/**
	 * @return whether the given fluid an instance of this fluid
	 */
	@Override
	public boolean matchesType(Fluid fluid) {
		return fluid == getStill() || fluid == getFlowing();
	}
 
	/**
	 * @return whether the fluid infinite like water
	 */
	@Override
	protected boolean isInfinite() {
		return false;
	}
 
	/**
	 * Perform actions when fluid flows into a replaceable block. Water drops
	 * the block's loot table. Lava plays the "block.lava.extinguish" sound.
	 */
	@Override
	protected void beforeBreakingBlock(WorldAccess world, BlockPos pos, BlockState state) {
		final BlockEntity blockEntity = state.hasBlockEntity() ? world.getBlockEntity(pos) : null;
		Block.dropStacks(state, world, pos, blockEntity);
	}
 
	/**
	 * Lava returns true if its FluidState is above a certain height and the
	 * Fluid is Water.
	 * 
	 * @return whether the given Fluid can flow into this FluidState
	 */
	@Override
	protected boolean canBeReplacedWith(FluidState fluidState, BlockView blockView, BlockPos blockPos, Fluid fluid, Direction direction) {
		return false;
	}
 
	/**
	 * Possibly related to the distance checks for flowing into nearby holes?
	 * Water returns 4. Lava returns 2 in the Overworld and 4 in the Nether.
	 */
	@Override
	protected int getFlowSpeed(WorldView worldView) {
		return 4;
	}
 
	/**
	 * Water returns 1. Lava returns 2 in the Overworld and 1 in the Nether.
	 */
	@Override
	protected int getLevelDecreasePerBlock(WorldView worldView) {
		return 1;
	}
 
	/**
	 * Water returns 5. Lava returns 30 in the Overworld and 10 in the Nether.
	 */
	@Override
	public int getTickRate(WorldView worldView) {
		return 5;
	}
 
	/**
	 * Water and Lava both return 100.0F.
	 */
	@Override
	protected float getBlastResistance() {
		return 100.0F;
	}
}

Now let's make an actual fluid which will have still and flowing variants. For this tutorial, we will call it Acid. The missing references will be filled in shortly.

public abstract class AcidFluid extends TutorialFluid {
	@Override
	public Fluid getStill() {
		return YOUR_STILL_FLUID_HERE;
	}
 
	@Override
	public Fluid getFlowing() {
		return YOUR_FLOWING_FLUID_HERE;
	}
 
	@Override
	public Item getBucketItem() {
		return YOUR_BUCKET_ITEM_HERE;
	}
 
	@Override
	protected BlockState toBlockState(FluidState fluidState) {
		return YOUR_FLUID_BLOCK_HERE.getDefaultState().with(Properties.LEVEL_15, getBlockStateLevel(fluidState));
	}
 
	public static class Flowing extends AcidFluid {
		@Override
		protected void appendProperties(StateManager.Builder<Fluid, FluidState> builder) {
			super.appendProperties(builder);
			builder.add(LEVEL);
		}
 
		@Override
		public int getLevel(FluidState fluidState) {
			return fluidState.get(LEVEL);
		}
 
		@Override
		public boolean isStill(FluidState fluidState) {
			return false;
		}
	}
 
	public static class Still extends AcidFluid {
		@Override
		public int getLevel(FluidState fluidState) {
			return 8;
		}
 
		@Override
		public boolean isStill(FluidState fluidState) {
			return true;
		}
	}
}

Next, we'll make static instances of still and flowing acid variants, and an acid bucket. In your ModInitializer:

public static FlowableFluid STILL_ACID;
public static FlowableFluid FLOWING_ACID;
public static Item ACID_BUCKET;
 
@Override
public void onInitialize() {
	STILL_ACID = Registry.register(Registry.FLUID, new Identifier(MOD_ID, "acid"), new AcidFluid.Still());
	FLOWING_ACID = Registry.register(Registry.FLUID, new Identifier(MOD_ID, "flowing_acid"), new AcidFluid.Flowing());
	ACID_BUCKET = Registry.register(Registry.ITEM, new Identifier(MOD_ID, "acid_bucket"), 
        new BucketItem(STILL_ACID, new Item.Settings().recipeRemainder(Items.BUCKET).maxCount(1)));
 
	// ...
}
 
// ...

To make a custom fluid behave more like water or lava, you must add it to a corresponding fluid tag: For water, make a data/minecraft/tags/fluids/water.json file and write the identifiers of your fluids in there:

{
	"replace": false,
	"values":
	[
		"your_mod_id:acid",
		"your_mod_id:flowing_acid"
	]
}

Next we need to create a block which will represent acid in the world. net.minecraft.block.FluidBlock is the class we need to use, but since its constructor is protected, we can't construct it directly. Some ways to use it are to make a subclass or an anonymous subclass. Here we will be showing the latter. In your ModInitializer:

public static Block ACID;
 
@Override
public void onInitialize() {
	ACID = Registry.register(Registry.BLOCK, new Identifier(MOD_ID, "acid"), new FluidBlock(STILL_ACID, FabricBlockSettings.copy(Blocks.WATER)){});
 
	// ...
} 

Now that we have these static objects, we can go back to AcidFluid and fill in the overridden methods:

public abstract class AcidFluid extends TutorialFluid {
	@Override
	public Fluid getStill() {
		return TutorialMod.STILL_ACID;
	}
 
	@Override
	public Fluid getFlowing() {
		return TutorialMod.FLOWING_ACID;
	}
 
	@Override
	public Item getBucketItem() {
		return TutorialMod.ACID_BUCKET;
	}
 
	@Override
	protected BlockState toBlockState(FluidState fluidState) {
		// getBlockStateLevel converts the LEVEL_1_8 of the fluid state to the LEVEL_15 the fluid block uses
		return TutorialMod.ACID.getDefaultState().with(Properties.LEVEL_15, getBlockStateLevel(fluidState));
	}
 
	public static class Flowing extends AcidFluid {
		@Override
		protected void appendProperties(StateManager.Builder<Fluid, FluidState> builder) {
			super.appendProperties(builder);
			builder.add(LEVEL);
		}
 
		@Override
		public int getLevel(FluidState fluidState) {
			return fluidState.get(LEVEL);
		}
 
		@Override
		public boolean isStill(FluidState fluidState) {
			return false;
		}
	}
 
	public static class Still extends AcidFluid {
		@Override
		public int getLevel(FluidState fluidState) {
			return 8;
		}
 
		@Override
		public boolean isStill(FluidState fluidState) {
			return true;
		}
	}
}  

For your fluids to have textures or be tinted with a color, you will need to register a FluidRenderHandler for them. Here, we will reuse water's textures and just change the tint color applied to them. To make sure the textures are rendered as translucent, you can use Fabric's BlockRenderLayerMap.

public class TutorialModClient implements ClientModInitializer {
 
	@Override
	public void onInitializeClient() {
		setupFluidRendering(TutorialMod.STILL_ACID, TutorialMod.FLOWING_ACID, new Identifier("minecraft", "water"), 0x4CC248);
		BlockRenderLayerMap.INSTANCE.putFluids(RenderLayer.getTranslucent(), TutorialMod.STILL_ACID, TutorialMod.FLOWING_ACID);
 
		// ...
	}
 
	public static void setupFluidRendering(final Fluid still, final Fluid flowing, final Identifier textureFluidId, final int color) {
		final Identifier stillSpriteId = new Identifier(textureFluidId.getNamespace(), "block/" + textureFluidId.getPath() + "_still");
		final Identifier flowingSpriteId = new Identifier(textureFluidId.getNamespace(), "block/" + textureFluidId.getPath() + "_flow");
 
		// If they're not already present, add the sprites to the block atlas
		ClientSpriteRegistryCallback.event(SpriteAtlasTexture.BLOCK_ATLAS_TEXTURE).register((atlasTexture, registry) -> {
			registry.register(stillSpriteId);
			registry.register(flowingSpriteId);
		});
 
		final Identifier fluidId = Registry.FLUID.getId(still);
		final Identifier listenerId = new Identifier(fluidId.getNamespace(), fluidId.getPath() + "_reload_listener");
 
		final Sprite[] fluidSprites = { null, null };
 
		ResourceManagerHelper.get(ResourceType.CLIENT_RESOURCES).registerReloadListener(new SimpleSynchronousResourceReloadListener() {
			@Override
			public Identifier getFabricId() {
				return listenerId;
			}
 
			/**
			 * Get the sprites from the block atlas when resources are reloaded
			 */
			@Override
			public void reload(ResourceManager resourceManager) {
				final Function<Identifier, Sprite> atlas = MinecraftClient.getInstance().getSpriteAtlas(SpriteAtlasTexture.BLOCK_ATLAS_TEXTURE);
				fluidSprites[0] = atlas.apply(stillSpriteId);
				fluidSprites[1] = atlas.apply(flowingSpriteId);
			}
		});
 
		// The FluidRenderer gets the sprites and color from a FluidRenderHandler during rendering
		final FluidRenderHandler renderHandler = new FluidRenderHandler()
		{
			@Override
			public Sprite[] getFluidSprites(BlockRenderView view, BlockPos pos, FluidState state) {
				return fluidSprites;
			}
 
			@Override
			public int getFluidColor(BlockRenderView view, BlockPos pos, FluidState state) {
				return color;
			}
		};
 
		FluidRenderHandlerRegistry.INSTANCE.register(still, renderHandler);
		FluidRenderHandlerRegistry.INSTANCE.register(flowing, renderHandler);
	}
}

If you want to use your own fluid textures, you can refer to vanilla's assets ¹⁾ as a template.

To make lakes of acid generate in the world, you can create a net.minecraft.world.gen.feature.LakeFeature in your ModInitializer and then add it to the biomes you want it to generate in:

public static LakeFeature ACID_LAKE;
 
@Override
public void onInitialize() {
	ACID_LAKE = Registry.register(Registry.FEATURE, new Identifier(MOD_ID, "acid_lake"), new LakeFeature(SingleStateFeatureConfig::deserialize));
 
	// generate in swamps, similar to water lakes, but with a chance of 40 (the higher the number, the lower the generation chance)
	Biomes.SWAMP.addFeature(
		GenerationStep.Feature.LOCAL_MODIFICATIONS,
		ACID_LAKE.configure(new SingleStateFeatureConfig(ACID.getDefaultState()))
			.createDecoratedFeature(Decorator.WATER_LAKE.configure(new ChanceDecoratorConfig(40)))
	);
}