Yes, SOLVER is a Scrabble word!

Letter values in Scrabble US: S 1, O 1, L 1, V 4, E 1, R 1.

Is it a valid word?

SOLVER is a valid word in the official Scrabble dictionary (US), the UK Scrabble Dictionary and Words with Friends (ENABLE).

a thinker who focuses on the problem as stated and tries to synthesize information and knowledge to achieve a solution

Also: problem solver, convergent thinker.