The sentence 'Studying is when I fall asleep' is an example of dangling modifier. When you read the sentence, you can tell that it does sound awkward. This is because the clause is not clearly related to the word it modifies. Who is studying? How is the action of studying related to the action of falling asleep? Unfortunately, you cannot correct dangling modifiers by simply moving it to a different place in the sentence. You will have to restate the sentence again by saying 'When I study, I fall asleep.' In that way, the doer of the action is clear and the clause gains meaning.
This one might be pretty common but it says "I like cooking my family and my pets" now that doesn't sound right at all but if you look at it with commas "I like cooking, my family, and my pets" now it might sound a little better.
