There is a clip to the left and right side of the keyboard. This clip hold the keyboard down along with the screws on the bottom. It is likely the clip has worn away and that would be why it keeps coming up. You would most likely need a new top cover to fix that but I would just get some adhesive to hold it down.

The Dell XPS M1530 has several documented issues with overheating. There is not a way to fix this issue without replacing the motherboard or reballing or replacing the GPU. There was a recall at some point involving the GPU but we are past that point now. Your best bet is to clean the unit out the best you can and turn some of the performance settings down to try to let it run as cool as possible. Clear out all the dust you can and if you feel comfortable, disassemble the unit and put new thermal paste on the unit. This will buy you sometime but the more your laptop shuts down due to thermal issues, the more it is dying. It will eventually give out and not be usable at all.

Does it do this when the adapter is not plugged in. A bad power cord could cause the computer to do that if so.