I am replacing the wall tiles in my shower, leaving the ceiling and floor tiles in place.

1. I have removed the wall tiles carefully. The cement backerboard is still in good shape and I would like to keep it. However, the dry, hard, carmel-coloured adhesive remains on the backerboard.

a) Can I tile right over the adhesive or will it be too bumpy leaving the tiles uneven?

b) If the adhesive has got to go, how do I get it off? Scraping, mineral spirits, and paint stripper have little effect. Grinding would likely remove the mesh covering the backerboard and make a big mess. Is there a solvent that won't make me pass out?

2. At the top of the wall the backerboard abuts directly to the finished ceiling tile. That means I can't tape that edge. Is that something I should worry about? Do I have to remove a row of ceiling tiles just so I can tape that edge?

Any help is appreciated.

Personally, I would strip it all out and install new backer board.
Sounds like old solvent based mastic. Your not going to get that stuff off.

How's about levelling the surface of the backerboard with Sheetrock 90?

DO NOT put any kind of sheetrock or drywall compound in a shower area.

If your set on using whats there then skim coat with a modified thinset mortar rated for cut-back adhesive application. I can't say for certain that this will work. It's your call.