New bathtub surround

[Cooler]

I am installing a new bathtub surround over an existing cast iron bathtub.

I have replaced the existing mineral wool insulation with fiberglass insulation and I have installed 6 mil plastic over the fiberglass. 

I have to install the cement backerboard. 

1. Do I allow the backer board to rest directly on the lip of the tub or do I leave a space (1/8" ??)?
   
2. Do I use silicone adhesive to adhere the 6 mil plastic sheet to the lip of the tub?
   
3. Do I leave an small gap between the tile and tub?
   
4. Do I use grout for that gap or silicone caulking?
   

I am not too worried about this installation as that bathroom is a guest bathroom and the shower has been used perhaps 5 or 6 times in the past 22 years.  (I don't get too many overnight guests.)

I am doing this for two reasons:  It keeps me busy enough that I don't go out of the house at all on the weekends, and it will help with the resale value of the house. 

(Our company is an "essential" business--we make components used by Department of Defense contractors and also components for the filtration business and they cannot produce drugs without that filtration so I am going to work during the week.)

[crokett™]

1. yes. actually I left it about 1/4 short so there was room for the tile to overhang the backer slightly and hide it.
2. i didn't, the backerboard would keep the plastic in place
3. yes
4. caulk, color matched if you can.