possible valve stem oil seals
Could also be piston rings. Excessive smoke *usually* means it's burning oil, so if that's the case there are faulty seals somewhere.
you need new valve seals in the heads or the choke on the carb isn't working right.
It's not warmed up yet.
Yes, but it can be hard on them if they are cold and not warmed up.
you need a new thermostat
the valve stem seals are probably dried up and leaking when engine is at rest
The transmission may not shift or engage in forward or reverse until the car warmed up for a few reasons. Two examples of why the transmission will not engage is low or no fluid levels or a leak.
Transmission is not shifting when car is warmed up.
Because in car language it is just waking up from the the frozen, uninsulated garage you put it in, and is cursing at with fowl car words.
You need to replace temperature sensor
If water is warmed up, then that means that its temperature does change.
The engine has to be running and warmed up for the heater to produce hot air. So yes, you need gasoline to get heat from your car (unless you have an electric car).
Problem with the choke or cold start injector system.