The flashback valve is a safty device of sorts. Inside is a fine wire mesh that works as a flame arrestor. Reason for this is that the vapor you see coming from the heads is oil vapor (if you run VERY rich it may also be fuel vapor that has diluted the oil) this vapor (being a petrolium by-product) is flameable. The flash back valve is ment to keep a back-fire in the intake from causing this vapor to ignite. I don't know if the explosion would simply blow out gaskets or split the case, either way it would be bad.
For the most part the only harm I can see leaving these hoses open (as far as I know) is 1. Oil vapor all over the engine, cloging not only the air filter but also insulating the engine with dirt causing it to run (a little) hotter. 2. Polluting the air. 3. Allowing water egress into the engine. A used flashback from Pelican must be cheap, I'd to it the right way.
Cold stalling could be a low idle (should be at 900-1000, use a tach dwell meter the dash tach won't do). Or the dwell is too small, or the points are bad, or the timing is retarded. Also see if the idle fuel adjustment is set too rich (little knob on top of the ECU) , or if the cold start valve is leaking causing a rich mix follow this link for more info.
http://www.914fan.net/
Step one: Get a tune up. New plugs,points, condensor, wires, set dwell (dwell meter $15-$25), timing ($20-$50 but most good timing lights are >$35), change the oil and add a snake oil to stop the oil burning, check the fuel mixture at a gas station. Make sure all the vac hoses are not leaking, if they are cracked at the ends chop them back until it is plyable rubber or replace them.