My engine is overheating?

It does not smoke at all. The engine will idle down to around 500 rpm's and shutter a little. But as soon as the rpm's get back around 700 or 800 it smooths out. I can let it run to what should be around regular temperature and hold my hand on the radiator and hoses. It is warm but nothing scolding hot. I can also lay my hand on the plenum and it's just warm. That's with the temperature gauge inside being 3/4 or more of the way up. But the hose from the coolant tank to the radiator seems cold so does the coolant in the tank. When you rev the engine you can see the coolant pull down a little but the coolant and hose does not seem to change temperature with the rest of the system.

I recently had a problem when I drove the car 2003 malibuand came home and parked it all the antifreeze would come poring out, brought to mechanic and he changed the thermostat. Brought the car home and it did it again, brought back to the mechanic and said the system need to be bled AND ANITI FREEZE CHANGED. Just drove it again today and it leaked but not as much when I opened the hood I noticed that the overflow bottle has a hose attached that is attached to nothing and that seems were today's leak came from is that hose supposed to be just loose and not attached to anything. Need advise please.

2003 Chevy Malibu had it flushed and changed ECT sensor. Now white smoke coming from tail pipe and rough idling.

Overheated three times and had to limp it home. It appears to do the overheating when you reach your destination and shut the car off would overflow through the overflow tank no water leaking anywhere else. The last time it overheated the engine shut off as I was driving.