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Sunken monastery:There are three doors with"three for one" sign and i don't know how to open the middle one, i have solved the book quest but still can't open it.
Abandoned mine: there is a gate to the "realm of the damned which i can't find the key to.
Do these gates have keys?or do i have to use my lockpick skills to pick them? Many thanks!

Monastary: all that door contains is another monster and a key. You'll only have to access this door if you chose the doors out of order.
Regarding your second question, there should be a key in there somewhere; make sure you check the whole mine.