There's no direct translation of I like cookies that doesn't change the meaning. One could say
gradisco i biscotti
but that's more similar to I appreciate cookies and sounds more formal than mi piacciono i biscotti. So it would be rather inappropriate to dub this way the Cookie Monster saying I like cookies.
The correct translation would indeed be mi piacciono i biscotti. Your question about the turtle should become
quanti pezzettini di torta piace mangiare alla tua tartaruga?
This adds another complication, because the subject seems plural, but is singular as the verbal form tells us: it's piace, not piacciono, because the subject is mangiare quanti pezzettini di torta, the infinitive mangiare is used as noun and so it requires the singular form for the verb.
Note that the word order in mangiare quanti pezzettini di torta is wrong, I used it just for clarity: the interrogative adjective quanti should come as soon as possible, leading to the correct order in the quoted question. In the case of a plain sentence, you'd say
alla mia tartaruga piace mangiare pezzettini di torta
again with a peculiar word order, the same as in mi piacciono i biscotti. Something like
i biscotti piacciono ad AsianSquirrel
is not ungrammatical, but not very common either, unless the sentence is in coordination with others: a complete analysis would be too long. To the contrary, something like
i biscotti piacciono molto ad AsianSquirrel
doesn't sound stranger than
ad AsianSquirrel piacciono molto i biscotti
ad AsianSquirrel i biscotti piacciono molto
because of the adverb.
The three forms have slight different emphasis on the various parts, but basically convey the same idea. The first form puts emphasis on the cookies, the second on the person who likes them, the third on the fact that AsianSquirrel likes cookies very much.