Diablo angel and demon name etymologies

You will not lose the gear that you have gathered.

You will lose save progress if you start at part 1, you can go back to the quests you already done (In your example 7 to 9).

The way the party system works is that you always enter the game at the level that the host is playing at. If they are further ahead of your character personally you will join them at part 7 (in your example).

When you go back to your own personal game, you can start back at part 1 but it will prompt you to save over your spot in the game. You can continue on from part 9, but you lose out on the story line in between.

What you can do is have your friend join you in your game and help you kill the butcher and jump ahead after that is done.

Edit image:

It's a little counter-intuitive, but the best way to tell is actually waypoints. When you abandon all question progress, you lose your checkpoint, location, etc. - any progress you may have made on your current quest. The consequence of that is that you'll need to go back to the last waypoint the next time you start that quest again.

There is a stipulation to that - for Act bosses, there is someone you talk to after defeating the boss to actually complete the entire quest. For example, after killing the Act I boss, there's actually a second quest before the next act (which consists of "talk to the person who takes you to the next act, and go to the next act").

I had this happen to be when I defeated the Act III boss - I recommend always either finding a waypoint or going to the next act before losing any current quest progress.