Shower – reuse the existing cement backer board when replacing tile in a shower

You don't tape the edges. Not on walls or tub. I'm not sure about a 1/4 inch gap by tub (probably would do 1/8 there) be everywhere else is fine. Nothing goes in the gap. Gap will be covered by either tile on the wall or baseboard.

Also make sure you are using the right mesh "tape". Your cement board gets same thinset as your tile .

That is pretty much it except waterproofing. The easiest way to do this is do your plastic**/backerboard first, then drywall, mud/tape/sand/, hit it with waterproof membrane***, then tile last.

** - I don't put plastic behind hardiboard unless I am afraid of water coming in from the other direction. With plastic if backer gets wet you are looking at longer dry times and the water most likely making its way down.

*** - You can use something like redgard. It paints on in about 20 mins and you do two coats. Its $50. Does a tub surround HAVE to have this. No. Would I suggest it. Hmmm. I don't know. This is determined by what is behind tub walls and materials. Hardiboard isn't going to let a small amount of water going through grout hit the other side. Some other brands of backer will (for instance durarock - which I would never use for showers but prefer for floors). If it is an outside wall, especially one that might be cold for a few months, I would be more apt to do the waterproofing. I just did a tub in my house a couple years ago and didn't. It is all inside walls and would have been overkill. (Old tile was on drywall that was in pristine condition after 50 years)

Another tip is to use the .5" hardiboard for tub. You will need to buy 4 sheets for a typical tub. They come in 3X5 sheets. You will simply stand each one up for each end. So backer will extend outside of the tub and 5 feet above it. You will then lie the back piece horizontally, and then cut your fourth at 2 feet to be even with the others. This advice is given you have standard American 5 foot tub. If you don't just make sure backer extends a few inches outside tub and goes about 5 feet higher than tub. For tiling I always recommend trying to tile past backer board so you have seamless transitions.