When do I use the following variations:

I didn't [verb in infinitive]

I haven't [verb in past participle].

I know that it has to do if it is a specific time (I didn't do) and a non-specific time (I haven't done), but I have seen (this time correct?)

Didn't in sentences where the time is not specified. For example here:

"I didn't see that coming" (see or saw? I think see),

"What did you do yesterday?" (But I think that one isn't correct, is it?)

or

"You didn't give me wings, but you showed me how to use them".

Thanks for your help.