Repairing wall near shower and floor - drywall repair
The first question is, has the leak been addressed? It’s difficult to tell from the photo the cause of the leak. If you feel it has been adequately fixed, then continue with your repair. What you’ve done looks good. The previous work inside the wall is not pretty. 

Next steps: Using fiberglass tiling tape, seal the seams between existing wallboard and new backerboard and between the two pieces you’ve installed. Apply mastic/mortar to match depth of existing wall board. Depending on the difference between the two surfaces, you may have to do two application of mortar to match depth. 

While you can use the tile mastic, Thinset mortar mix is somewhat better for this application. The difference is the bond created. The mastic makes a chemical bond and the mortar makes a mechanical bond. Regardless, make sure to seal up all exposed area. Allow all new seams to dry completely before next steps. 

Once dry, you can now reset the tiles. Be certain to use a notched trowel to apply mortar/mastic for proper setting and curing. The notches provide air into the joint to facilitate curing. After reset is dry, clean area with a tile sponge and plain water. Grout as normal, let dry. Use a premium grout sealer on new install, then a silicone caulking around all tile and to the shower, making certain any old caulking has been removed. 

Use joint compound on area not covered by tile. Apply skimcoat of compound over the mortar/mastic you have previously applied, and texture to match existing wall. Sand, and paint as usual. 

Finally, I recommend getting a hand steamer to throughly clean and restore the shower rails and existing grout. It really works well to rid all fungus stain and lime build-up without chemicals which will degrade new and existing grout. I use my steamer to clean multiple surfaces; best cleaning tool investment ever.