For #1 I would blame linux. It's bluetooth stack is... let's say less than stellar, expecially for headsets. I always have to fiddle to get my headset to work, while it works perfectly with any other OS I tried (MacOS, iOS, Android, Windows).

#2: True, but usually the battery of a pair of headphones last much longer than earbuds, in my case at least 4 days, so I just put them in charge at night