Congrats for your purchase.
for your first query please visit any 3S dealer preferably Hyundai Sowan Motors, and tell them the exact RPM problem, they will diagnose and tell you the problem, it might be a clogged or dirty sensor they will clean for good.
for your second question, there is no Check Engine Light in my santro 3003 as well, and people say there is no sensor in 2003 santro.
and engine tuning include also air filter cleaning, and spark plug cleaning, alongwith other stuff you have mentioned like tappet adjustment
rest the expert will shed some light.