Yes u can just change the tires without changing the rim....i did on mine old mtb running on 26" 1.95 tires to 1.25 with lesser thread....my speed increase from 14kmh to 22kmh....extra to note off, if u change tires psi to pump also will change depend on the tires...mayb higher....like me last time was psi 60 now was 100psi...
Slick tires (tires with smooth surface and little pattern) will roll faster. If you want thin slicks you can consider the Schwalbe Kojak.
But me personally I would go the other way. Buy fatter tires but also slick patterns, like the Schwalbe Big Apple. Wider tires roll faster because they absorb road imperfections better. Also they are more comfortable. Currently Big Apples (size 406) are 80 for a pair on the togoparts market.
Alot of those cheaper stock rims wont take 100psi, wider mtb rims wont either. They can be quite dangerous when they fail, they either bend and the tire blows out or they splt and fail and ther tire blows off.
The original tires stated max weight 65kg which is very low right? I'm planning to get slimmer tires so that it can go faster. If the new tires psi rating is 100, can I pump to that level with my original rims?
I wouldn't risk it rims have a pressure rating as well as tires, on a cheap bike if it is not stated on the rim they are probably roughly the same as the original tires max rating. 14 or 15mm internal width roadie clincher rims are usually good up to 120psi. My 28mm mtb rims are 50max. the tire may not blow off straight away but if you heat up the rim from braking or start to wear the brake track then there is a chance it could go bang when you are riding. I wouldn't risk taking those cheap aluminum rims up to 100psi Also make sure that the tire you get is minimum width the external width of the rim