There a re few threads already on these that you might want to search. Here are a couple good ones with info: Librem 5 Supported Temperature Range - #13 by dos and It's a burning phone - #16 by fiacco Based on your description it’s hard to tell. An since it has been a while, just to check, which modem [wifi card] are you using (did you replace it - that may have little bearing)?
On #1: I hope you’ve done your updates as those have cooled L5 down since what it was years in the early days. Still, L5 does get a bit warm in normal use. The Mobile Settings app has “liberem 5” tab that has temperature sensor readings of the various parts (CPU, GPU, VPU, Fuel Gauge, Battery) [no, I have no idea what the “Fuel Gauge” one is - maybe mislabelled charging temp]. When I start up, the first three are about 34-36’C in idle and battery at 28’C in about 27’C ambient room temperature. I use a printed plastic case and normal light use hasn’t become problem as temps increases about 10’C on all, but I too share the notion and worry that in certain situations I should remove it. As I’ve understood, the internal temps can rise safely well beyond 50’C but I haven’t measured how warm that would feel out side of L5, so hard to say what you limit for felt heat is. There are scripts to halt the L5 in unsafe temps (but can’t remember was it ever talked about what those limits are).
So, if you want to dig deeper on if your specific situation is normal, I’d suggest looking at some temperature numbers and defining hot. It may be normal, it may not. Yes, on your second thing, if there is a heat problem, it could easily influence stability. But again on that, I hope you’ve updated after your brake.
As an extra: there’s a thread about adding a bit of ZRAM, which may have temperature benefits as well as it may lower work cycles: Why and how to extend ZRAM on L5. A revolution for Librem 5 stability!