Almost sounds like a bent shift fork or heavily worn shift drum (more likely the fork). Generally if it's the clutch, you'd notice the slipping more in high gears instead of low gears and the transaction between slipping and grabbing is pretty smooth, kind of like driving a stick car. The "clutch adjustment" screw is to adjust when the trans clutch is used as you shift, atleast that's how it works for the 250es/sx machines, if it shifts between gears fine, the adjuster doesn't do anything else unless too tight it could make it slip all the time.
The high/low range selector popping out of gear isn't normal. I didn't have a 110 to ride, but I've road around a 90, and it never popped out. Maybe it's not fully switched into high? My 200es high/low was a little tricky to get into high range sometimes and rocking the machine would get it locked in. Since then if I remember correctly, neutral, shift into high, then while pushing forward shift into 1st gear would lock it in every time, but I haven't taken that machine for a ride in probably 5-6 years since I got a 250es and 350x.
What year is your 110? I have two
parts machines that should have good bottom ends if you do find out what's causing it and need
parts.
Good luck with your project