If resistance increases, does voltage increase or decrease? And why?
Generally if you're talking about a resistor in series, then yes, the voltage will increase. It's not just because of the formula V=IR.
Consider a circuit with a certain resistor of resistance R and let the rest of the circuit have resistance R', for a total effective resistance R+R'. Then, the current is V/(R+R'), so the voltage over the resistor R is RV/(R+R') = V*(1-R')/(R+R'). Here, as R' is a constant, if we increase R', we decrease the value of the fraction to be subtracted, thus increasing the voltage of the resistor. THAT is why voltage normally increases.
However, if you have resistors in parallel, the resistance will not affect the voltage over the resistor (if it's the only resistor and no other resistor is in series with it).