I noticed that the time he vomits usually vomits after having a meal.

“The time” is not needed here. I also put “usually” in a place that sounds more natural, but your original sentence is correct.

Previously, the former owner gave freeze-dried chicken, cat grass biscuits, and canned cat food as staple food for Bao.

Especially the freeze-dried chicken and cat grass were brought from an individual seller store on Pinduoduo.

“Especially” doesn’t really make sense in this context. Especially is kind of used to highlight a certain quality.
Ex: The food for Bao is not that reliable, especially the freeze-dried chicken and cat grass which were bought from an individual seller store on Pinduoduo.

(Pinduoduo is just like Amazon whichere the price of most goods are not very expensive.)

Later I searched for the reason fors that cats vomit and found that it's not good for cats to eat too varied of a diet.

Also, the quality of freeze-dried chicken sold by the individual seller stores is usually is not good.

This sounds more natural. I would only say “sold by the individual seller store” if you’re talking about the specific one you buy Bao’s food from, but it sounds like you are talking about individual sellers as a whole.

If cats don't feel well they will vomit something like hairballs by having some cat grass instinctively.

Im not exactly sure what this sentence means. It sounds like they will instinctively eat cat grass to make themselves vomit to me. I think you are trying to say “If cats don’t feel well after eating cat grass, they will instinctively vomit something like hairballs.”

On the contrary, consuming too many cat grass biscuits will lead cats to vomit frequently.

It kinda doesn’t make sense to say “on the contrary” here because the whole text supports the idea that cat grass will make cats vomit.

So I searched fora lots of relative knowledge for relevant information and observed him for some time.

'relevant' rather than 'relative'. I would say 'information' not 'knowledge'. 'knowledge' is not really correct here.

I noticed, that the time he vomits usually vomits is after having a meal.

Previously the former owner gaHis former owner had previously given freeze-dried chicken, cat grass biscuits, and canned cat food as staple food for Bao.

Especially the freeze-dried chicken and cat grass, which were brought from an individual seller store on Pinduoduo.

Need a relative pronoun needed to link the two clauses together.

(Pinduoduo is just like Amazon whichere the price of most goods are not very expensive.)

Virtual location use 'where'.

Later I searched for the reason for a cat vomiting and found that it's not good for cats to eat too varied a diet.

'cat vomit' would be a noun phrase and is a thing not an action.

Also, the quality of freeze-dried chicken sold by the individual seller store is usually is not good.

If cats don't feel well, they will vomit up something like hairballs by havinstinctively eating some cat grass instinctively.

Cats don't voluntarily eat cat grass biscuits and even have no idea that there is cat grass in biscuits.

On the contrary, consuming too many cat grass biscuits will lead to cats to vomiting frequently.

I noticed that the time he vomits usually vomits is after having a meal.

I added the word, "is."
I also moved the word "usually" to modify "vomits" rather than "after having a meal." "Usually" means it happens a lot but not every time. I'm assuming that Bao does not vomit every time he eats.