So I just rebuilt my engine and everything.

So I just rebuilt my engine and everything sounds in tune but I've noticed a few things. (1) ever time I start it cold it warms up fine and about a min or 2 later a little white smoke comes out the exhaust and then goes away so I'd believe that to be condensation. (2) when I start to drive the car it drives fine but the temp gauge starts to go up but never has gone over 3/4s of the way and it will drop down to normal. Also it will drop to normal wen I start moving. And it only does this when I have the heater off with heater on it stays cool and no sweet smell coming from exhaust or from vents. (3) this is the last thing. Every time I drive somewhere and turn my car off from anywhere between 5min-1hour it will start up but just idle really low like it wants to die but if I give it some gas I get a cloud of smoke like I would if I did a fuel system cleaning and it comes back to a normal idle and smoke goes away.(4) once I let my car cool over night I have to check my coolant in the radiator and it seems like its a little low like just a little below the upper radiator hose my over flow resivor is full and I no longer have any leaks as of yesterday that I know of I'm going to check today to see if I stil have that issue. But if so idk where it is losing coolant


Please any input would help a lot.