2009 outback coolant issue

have a 2009 outback ... step daughter ran it without coolant (where it went is another issue) and I believe got it hot ... engine light on (coolant was the only problem I could find without actually tearing it down) ... filled it with coolant and started it ... cool air coming out of the vent ... drove it a short distance (two blocks) and it got hot ... not all the way in the red but close ... shut it off ... burped the radiator and let it cool down a little ... started it and heat coming from the vents now ... drove 5-10 miles and temp gauge stayed about half way like normal .. however the engine light is still on

1. do I have another problem (other than where did the coolant go)
2. do I still need to read the code for the light (or will it go off after so many starts
3. is it safe to drive now ... seems to be running pretty good

any info will help TIA