Yes you can increase speed by Installing relay any electrition can try it for you if Relay can make a difference.
Better fan you can find from Bilal gunj.
But make sure its not a normal denso fan and its a 12 blade one powerful one. And no it will not be a bolt on you will have to do little alteration but that is a very minor kind of alteration.
If i was in your place i would go to bilal gunj and look for better radiator as well that comes with the fan. (Some Experts might not agree with this approach) but thats how i fixed my previous car 1000cc I installed 3 channel radiator and never had heating issues.