[Grammar] should, were to, happen to

[BDX777]

Here is a piece of grammar book, which I hope quoted correctly, "when we use "should" after if, this makes the possibility of an event seem unlikely"
My question is what for. Why do we create sentece like "If you should see Ann, could you ask her to call me?". If we can use "if you saw Ann, would you ask her to call me?"
And here "If I were to ask you to marry me, what would you do?" when we can use "If I asked you to marry me, what would you do?"

"happen to" this emphasises chance possibilities
Does it mean "If you happen to go to a shop, buy me some food" has more chance to be done than " If you go to a shop, buy me some food"

 

[Raymott]

"If you should see Ann ..." means "If you happen to see Ann ...", which for practical purposes means, "If you [do] see Ann ...". 'Do' is emphasised if it's used. "If you saw Ann ..." doesn't work. If you saw Ann in the past, you can't ask her anything now.

A: If you see Ann, can you ask her to call me?
B: I don't think I'll see Ann.
A: No, but if you just happen to ... If you do see her ...

'Happen to'. You might say that if you're less sure, as above.

"If I were to ask you to marry me ..." means "If I asked you to marry me ...". It's just another way of saying it.
You never have to use "If you should ..." I don't.

 

[BDX777]

'Happen to'. You might say that if you're less sure, as above.

Does "happen to" have similar meaning to second conditional?

 

[jutfrank]

Does "happen to" have similar meaning to second conditional?

It's more often used in first (real) conditionals, than second (unreal).