Feel the top of your PlayStation.. is it hot? Also I think to get rid of the flashing problem you just got to keep holding the PS button.. the reason why your PS4 might not be turning on is because a cord might not be properly put in the back of your TV I don't know everything.. I hope this helps a bit..
It might be the cord that goes into the muffs.. I don't know if I have this problem to, but that's probably it because it might make like a scratching noise?
How much have you been using your Nintendo switch? If you don't use it a lot.. I'm not 100% sure.. if you do use it a lot.. then limit your usage, because it might overheat.. I hope this helps at least a bit..
I don't really have an answer for this but one thing that can temporarily fix it is by like every 10 seconds manually turn off your tablet then turn it back on and then continue playing, and then turn it off and then turn it back on. For now it's worked for me.. but I don't know if I have the same problem as you.