This is only special cases of the form and use of the questions tags. To learn about the basics go here first:

Question Tags: The Basics.

I AM

The negative question tag "am I not" has no contraction. Because a question tag with no contraction sounds very pedantic, we prefer a very ungrammatical constraction but which is correct for question tags: "aren't I?"

- I'm late, aren't I?
- I'm talking to the walls, aren't I?
 
SUGGESTIONS

After a sentence with Let's... we use "shall we?"
 
- Let's go out for a walk, shall we?
- Let's study tomorrow morning, shall we?

IMPERATIVES & INVITATIONS

After an imperative we use "will you?" (always affirmative). We can consider "will you?" as an equivalent to "please" (more or less)
 
- Open the door, will you?
- Don't smoke in this room, will you?
- Come to my party, will you?
- Have a coffee, will you?
- Don't look at me like that, will you?

 THERE IS, etc.

In the impersonal construction to show existence (there is/are/will be, etc.) THERE acts as the subject of the question tag too.

- There are two cats in the roof, are't there?
- There wasn't a lion in the park, was there?

SAME-WAY QUESTION TAGS

We can use an affirmative question tag with an affirmative sentence and with a falling intonation. We use these same-way question tags when we are just repeating what somebody said (maybe even the listener), so we are not asking a question or looking for confirmation, we are simply repeating information to express interest, surprise, concern or some other reaction.

Compare:

- David is your boyfriend, isn't he? ↗  (I think he is, but I'm not sure)
- Oh yes, he's my boyfriend

- David is your boyfriend, is he? ↘  (I know perfectly well, I just want to let you know that I know)
- Well, yes. Who told you?
- Oh, everybody knows now

- Hello, I'm Tim. I will be your student this year.
- Oh, so you will be my student, will you?
- Yes, nice to meet you, sir.

More examples:

- Mary will come later, will she?
- You're Kevin Bratson, are you?
- Oh, so this is your house, is it?
- So you're having a baby soon, are you? Congratulations!
- Oh, he thinks he is the best, is he? Come on, when will he grow up!
- You're father's at home, is he? Can I come in?

We can also have a negative sentence with a negative question tag, but that is a lot of negativeness and it sounds aggressive:

- Oh, I heard that you don't like my house, don't you? ↘
- You're not very nice, aren't you? ↘

If there are two verbs in the sentence, the question tag may refer to one or the other, you must use your common sense here:

- I think you're John, aren't you? (= are you John?)
- I think you're John, don't I (= do I think...?)  [this would be correct but very rare]