the usage of "why not"

[Sweetpumpkin]

Hello,

1) "Why not", as far as I know, it is used as its literal meaning. For example:

A: I can't go to the party tonight.
B: Why not?(=Why can't you go there?)

Do you think my example makes sense :( Anyway... am I right?

2) It can be used as almost same as "sure". For example:

A: Do you mind if I turned on the air conditioner?
B: Why not?

or

A: Can I turn down the radio?
B: Why not?

3) Can "why not?" be same as "Why don't you~"(suggestion)? For example:

Why don't you go shopping with me?
Why not go shopping with me?

What do you say? Are they almost same?

4) I made those examples. If there are mistakes, please correct me! Is there another usage of "why not"? If there is, please let me know.

Thank you for your attentions in advance,
sweetpumpkin

[Molly]