1. The animal eats one kilogram of plant every day.

1-1. The animal eats one kilogram of plants every day.

2. The animal eats one kind of plant every day.

3. The animal eats many kinds of plant every day.

4. The animal eats many kinds of plants every day.

5. The animal eats a liter of plant every day.

(Are they all grammatical? Do we have to use the singular form 'plant' or the plural form 'plants' in the sentences?)

1, 3, 5 = no

1-1, 2, 4 = yes

If I refer to one day lily, I'd be referring to one plant. But if I'm not referring to any one plant in particular, then I need to use the collective plural, plants.

http://grammar.ccc.commnet.edu/grammar/plurals.htm#collective_nouns

All of the sentences you provided are grammatically correct, but choosing between the singular form "plant" and the plural form "plants" depends on the intended meaning.

1. The animal eats one kilogram of plant every day.
- In this sentence, "plant" is used as a mass noun, referring to a non-countable substance, like grass or foliage. It means that the animal consumes one kilogram of plant matter in total.

1-1. The animal eats one kilogram of plants every day.
- This sentence uses the plural form "plants," suggesting that the animal consumes multiple individual plants with a combined weight of one kilogram. Each plant may be smaller than a kilogram, but in total, they add up to one kilogram.

2. The animal eats one kind of plant every day.
- Here, the singular form "plant" is used to indicate that the animal consumes a single type or species of plant every day.

3. The animal eats many kinds of plant every day.
- Similarly, this sentence uses the singular form "plant" to highlight the fact that the animal consumes multiple types or species of plants each day. Instances of individual plants are not specified.

4. The animal eats many kinds of plants every day.
- In contrast to the previous sentence, here the plural form "plants" is used to convey that the animal consumes multiple individual plants of various types or species every day.

5. The animal eats a liter of plant every day.
- Similar to the first example, "plant" is used as a mass noun in the singular form, indicating that the animal consumes one liter of plant matter in total.

In summary, the choice between using the singular form "plant" or the plural form "plants" depends on whether you want to emphasize the total quantity of plant matter (using singular form) or multiple individual instances of plants (using plural form).