Is it enough to evaluate a person on a 2-3 hour basis test or one should be tested on a 2-3 month probation to know his/her strengths and weaknesses?

it is not%, but you can determine the headlines and as per that you will expect the right person then3 month as work try to find if ok

It depends on the test, but for a good check2 months is a good time and definitely you could get an entire range of personal qualities

It depends on the skill you want to test. For example, if it is skill in AutoCAD,2-3 hours will be quite enough. 

However, to evaluate his/her strengths and weaknesses, several months will be needed.

You can never tell how a new employee will work out - it takes several months before you know.