Hi!
Ofcourse your OS .35 can idle for more a minute without problem...! It should be able to idle fine for 5-10 minutes or more and roar to life when you give full trottle.

Have you check the fuelneedle for dirt???
A starting point for the highspeed needle is 2 turns open.
The screw that controls the hole opening at the front of the carb is the idle screw.
The third screw you speak of is the screw pointing straight up and that screw is the screw that holds the throttle drum in place.
The idle screw or low speed needle controls the amount of air coming into the engine at idle/low speed (when the throttle drum is at idle/low speed and only then).
This idle screw should be set so the round opening at the front of the carb is half open.This is the starting point and can of course be changed. More open means more air is coming into the engine. More closed means less air, which also means that the engine runs richer at low speed.

Here it is vital that you know HOW your engine sounds and reacts when you set the idle.
If the engine hesitates and nearly dies when you give full power, then the idle mixture is too lean, if on the other hand the engine hesitates and bluddersand sputters fuel..then the idle needle is set too rich. Remember...there is also some interaction between the highspeed and low sped needle.
Regards!
Jan K
Sweden