Diablo – Does follower equipment carry over difficulties

If players are within 4 levels of each other, experience is worth 100%. Starting at 5+ levels apart, experience decreases by 10% each level until it reaches 10+ levels apart, it then decreases by 95%.

Example: a level 1 being boosted by a level 60 will still receive 5% XP per monster kill.

However, if you legitimately kill monsters in a more difficult act with friends your own level (or solo) you receive the full amount of XP.

No solid citations yet, sorry.

Chris Rasys is right.

While some achievements are character specific, the criteria for the lore and bestiary achievements (and others) are not. This means you can complete each individual task with a separate character if need be, and you will still unlock the achievement in the end.

So in this case, your solution is simple: Start a new character (of a different class, or Hardcore, perhaps!) and play through Act I again. You should pick up the missing pieces and round out your achievement.