In an unambiguous grammar, do left and right derivation both produce the same parse tree? Because I have read that grammar having more than one parse tree is said to be ambiguous.
If the grammar is unambiguous, there is only one parse tree. (By definition.) So the leftmost and rightmost derivations generate the same tree.
You can think of a derivation as a tree walk. For a given tree, there are many different possible ways of traversing it. Leftmost and rightmost derivations are pre- and post-order depth-first traverses, respectively.