About 2 decades ago, maybe longer you could damage a monitor like that but times have changed and at worst it just won't work.
As to the stick, it's your money. Try it.
I currently own an Amazon Fire TV Stick and was wondering what would happen if I set the stick to 720p 50Hz on my current 60Hz 720p HDTV. If I run the refresh rate of 50Hz on a 60Hz television, will this ruin the hardware or permanent function of the television and/or the Fire TV Stick?? I want to test 50Hz on my 60Hz television to see what happens with the picture. If I'm not pleased, can I just switch the settings back to 60Hz without any permanent harm to my television or Fire TV Stick?