You might try a method I found to work sometimes, writing a nice (honest) letter to their customer support telling them how much you enjoy their product but sadly you are missing said screws. With a bit of luck you will get a thank you in reply along with a new set of screws in the mail. Depends on the manufacturer of course, but some companies value the positive customer relations over any “effort” that might take.
The microchip only has so much surface to exchange heat with the air, so even if the airflow is good, thermal paste or a heat sink often are required to conduct the heat away from the chip to then be transferred into the airflow (convection).
It should be possible to replace the battery, given that the device itself has not taken any permanent damage (deformation or rupture of the frame, torn cables, etc.). If the glue of the screen separated, it would be best if it was replaced. As for the battery having inflated, this damaged LiPo battery should be disposed of safely ASAP. Check for a special disposal location near you and transport it safely there (no metal container that could short the battery, no sharp edges that could tear / puncture it). Put it somewhere where you could possibly get rid of it fast and as safely as possible if it should catch fire.