• student’s sentence
• Teacher’s suggestions
• Correction

He likes to runs.
He (subj) likes (verb) [to run] (object)。 To + verb = noun (Infinitive,即动词不定式,通过在动词原形前加to,创造一个具有名词性特质的短语)
第三人称单数作主语,其后动词加s(likes),但like的对象用「to do」动词不定式结构表示,这里的动词run是不需要加s的。
He likes to run.

She contempts to feeds the cat.
contempt?or{attempt}?. Again,{to do}动词不定式结构的动词feed不可以加s.
She attempts to feed the cat.

My dog catchs a stick.
第三人称单数作主语,其后动词以-s/-ss/-sh/-ch结尾,要加es.
My dog catches a stick.

We admire animals.
admire一般用于形容对「人」的敬佩和仰慕,对动物我们一般可以使用adore搭配,表示喜爱.
We adore animals.

He eats apple.
{apple} is a countable noun.You should use {an apple} or {apples} here instead.
He eats an apple.

She cooks pizza.
做披萨饼一般使用动词bake/make/order搭配pizza,不用cook搭配.
She bakes pizza.

Cats loves to eats fish.
Cats是复数名词,不需要在它的动词后加s.Again,{to do}动词不定式结构的动词eat不可以加s.
Cats love to eat fish.