When I am running Ubuntu 20.04 from a live USB (without installing it) it usually happens that when a certain degree of activity is reached (i.e lots of programs running and/or lot of internet tabs with videos at the same time) or a lot of memory is used (many downloads, for example) the laptop freezes totally and I am forced to turn off it by pressing the power button (no solutions like the ones exposed here work).
As I have resigned myself to it I would like at least to know if I can monitor that process in any way: i.e. if I can check any indicator or program which tell me that the activity has reached certain level that makes this freezing likely (I don't know which one is exactly the parameter I should check, I guess the RAM memory, but not sure)
free. Ubuntu tries to run in RAM if not enough RAM things slow down, You did not mention how you made the USB. If it is booting ISO files stored on a NTFS partition it will not power off.