CodeChef Ratings

Should I need to solve all questions in contests to improve my ratings or partially 3/7 solved problems will also help in increasing my ratings ?

It depends upon your rank and not on number of problems solved . If you are able to solve 5/7 problems in div 4 then you can get a good rank(it also depends upon contest also like whether it is cookoff,lunchtime or any other).
codechef has mentioned full procedure how the calculate ratings you can read this link below: