It's different for exercise because that's a verb as well. I'd just say "Why do you exercise?"
As far as quotation marks go, if the question mark is part of the quote then the question mark goes inside the quotation marks. If it's part of the sentence outside the quote, it goes outside.
I want to know if "How are you?" is correct.
Is there a problem with the sentence "I have a cat"?
If you're giving us a list of complete sentences to read, you don't need to put any of them in quotation marks.
1. Where is the prison?
2. I want to know where the prison is.
You won't get a consensus of opinion on whether to use single or double quotation marks. On the forum, I use only double quotation marks, whether it's for direct speech or when I'm exemplifying a word or sentence etc. That is entirely because I find single quotes quite hard to see in a post, even on a laptop (on my mobile, they're almost invisible). A double quotation mark is hard to miss. It gets more complicated when you want to put a quote within a quote but I don't think we need to worry about that right now. So you can choose to put a single quotation mark (one key stroke, using the same key you use for an apostrophe) or you can use double quotation marks (one key stroke, using the key that actually shows the double quotation marks on it). What you should not do is type a single quotation mark twice in succession in order to make something that looks like a double quotation mark but actually isn't one.
The key you need to use will depend on your keyboard. If you've got a standard PC/laptop keyboard, the double quotation mark is above the number 2. You need to hold down the Shift key and hit the 2. If you've got an Apple desktop or a Mac laptop, the double quotation mark is above the apostrophe - hold down Shift and hit the apostrophe key.
Here's where it is on a PC keyboard:
Here's where it is on a Mac keyboard: