Don't think you are getting alot of independent thinking on this issue, it is just me.
Judgement on the time it takes to heat up to engine depends on the outside temperature and the driving speed. If you have a 4 cyl, I would guess in 30 degree weather, driving at 40 mph, the engine should heat to the middle of the dial (operating temperature) in 5 - 10 min. Maybe someone with exactly your car can give a better estimate.
As far as the blocked heater core goes, I would make sure your thermostat is good first, then with the engine off, turn on the heater and disconnect the heater return hose. When you turn on the engine, coolant should flow out of the hose rather quickly unless the thermostat also cuts off flow to the heater. In that case, you will get coolant flow to the heater only after the thermostat opens. Turn the engine off immediately after you start to loose coolant. Reconnect the hose. If the flow is only a trickle, then it is likely that your core is blocked.
I think it is likely to be the core if your thermostat is good. I am not sure how to test the heater valve. It would depend on how your heater is set up.