Did you send it to Verizon or did you contact the manufacturer? Definitely contact one or both of them again as clearly the battery replacement didn't address the issue
107 is perfectly fine. My G2 hits 115-125 during intense operations and that is acceptable. Charging creates a lot of heat. Some don't notice this due to cases on the phone which hold in heat, yet keep the user from feeling the heat.
Looks like the opinions on this as far as the G3 vary with some saying its normal and some saying its too hot. No clue but if it's affecting performance or shutting down then that would be the time to be a little alarmed I guess.
Shutting off or going into protection mode yes, but otherwise, I believe normal. Consider the G2 and Turbo that turbo charge x amount in 15 min. If I didn't have a case on my G2, I wouldn't want to hold it long, and it's 2 years old so, in my case, I'm confident. Different for all kinds I guess.