1-- Yes. Mixed conditionals are common.
2-- Your sentence is not Conditional II, but the answer is the same as for #1
3-- Mixed conditional
4-- Zero conditional is for general truths; ‘if’ can be replaced by ‘when’. Are you so sure about the coming rain?
Note: Mixed conditionals occur a lot in speech and when future events occur in the main clause, but they are still usually avoided in careful English.
As I understand it, a mixed conditional takes into account the time of each clause:
If I had studied (Cond III) more in university, I would make (Cond II) more money now.
If I was a better student, I may not have so much trouble at school in the future.-- I suppose on 2nd thought that it is indeed a mixed conditional too, but it is muddied for me by the fact that indicative ‘was’ is not generally accepted as a substitute for the more careful subjunctive ‘were’; it is still considered casual by many grammarians.