A professional installer would use a pair of scribes to transfer the contour of the wall onto the top edge of the counter top then use a circular saw or a belt sander to take off the area of the backsplash where your wall is bowed out.
How to install tile backsplash on uneven wall.
This ensures the tile adhesive secures to the surface.
Apply grout with a rubber float working diagonally across the tile.
Spread the mortar with the flat edge of the trowel then groove.
Wash the wall with tsp tri sodium phosphate or an ammonia based cleaner to remove any grease or oil.
Slightly rock the sheet up and down perpendicular to the trowel lines to collapse the ridges and help the tile settle into place.
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Mark the two sides of the wall using the painter s tape where the backsplash should.
Hold a tile at this spot accounting for a 1 8 inch expansion gap.
Do not grout the bottom seam where the tile meets the countertop you ll want to use caulk in that seam.
Place the mosaic sheets along the wall.
Then use a level to extend the line along the work area.
While you volunteered to set tiles is repairing rebuilding the wall something you even want to deal with.
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Like bill pointed out you are unlikely to end up with a flat enough surface to get a good tile job unless you use very small tiles.
Follow the lines you made when the tiles were dry fit to the wall.
Learn how to install a tile backsplash.
First use a level to find the lowest point of the countertop.
1 4 inch is not too much to take off provided your cabinets do not measure anymore than 24 from wall to front of face frame.
Use the float to take off any excess grout then allow the grout to set for 10 minutes.
Use tile spacers if necessary to keep the tile lines straight in the layout.
Backsplash installation in 15 steps.
Spread thinset mortar on the bottom center of the wall.
Add tile spacers for help keeping the tile pieces lined up.
Mark the wall at the top of the tile.
Clean the wall thoroughly with the cleaner to remove any grease or other debris.
That is what i would do so it could be painted i would not even try to tile over the patch job you described.
Hold the float at a 45 degree angle as you work the grout into the seams.
Secure the drop cloth on the counter using the painter s tape covering the entire work area.
Ready to get started.
If existing tiles are beyond repair remove the tile and install a piece of wallboard in its place.