Basketball, Be the best player on the worst team not only would my contracts be big because the team would need me and i’d be a all star
This is just a personal question, answer what you think
I believe the last one. A dangling modifier is a word or phrase that defines something or someone not spoken about in the sentence. So "a successful career as an author seemed certain", but seemed certain to who? A fair warning: I could be wrong.
The sentence has two clauses: "Please watch the babies" and "while Mother takes a nap". (You didn't underline a clause so I'm going to explain both of them).
First Clause: "Please watch the babies"
This is an independent clause. You can identify independent clauses when you read it and it has a full idea already. It can stand without another clause to back it up.
Second Clause: "while Mother takes a nap"
This is a subordinate clause. Subordinate clauses usually start with a conjunction. You'll see that the given clause starts with "while", which is a conjunction.