1- 'Should can be used in first conditionals in two ways:
If you should see her, please tell her I called.
Should you see her, please tell her I called.
The second shows that the answer to your question is yes.
2 Second conditional inversion is less common, and mostly found in formal language:
If you were to win...
Were you to win
You don't hear it that much in speech because it isn't very easy to say.
3 You can use 'would' after 'if', but there has to be a reason for doing it. If you are negotiating with someone, the use of 'would' in both halves of the sentence acts to balance things, making the person likely to agree, so you will also see it in requests sometimes:
If you would be so kind as to...
I would be grateful if you would...