As a professional tiler of over 27 years I've done countless tiles over all sorts of situations. Tile over tile or glass can be one of the smartest, least stressful and most economical ways without compromise to quality.
Firstly I would recommend getting the old glue and white set off. As the new glue dries under the tiles it can tend to pull off the existing white set or glue. Once you have got as much off as possible then definitely prime your surface. The only time primer will go a white gluggy mess is if you start tiling when the primer is still wet.
Priming over a dusty surface is essential. Doing a skin coat of glue is a good idea to get the surfaces flat.
What we used to do is work out the deepest spots, circle them, notch trowel the area and with a level we would screed the glue flat then steel float it with the back of your notch trowel. Then allow the glue 12-24 hours drying time before tiling.
Please don't use silicone. Big no no. Best thing to do is give your glass splash back a good clean with sugar soap. Then dry and wipe over with some methylated spirits. What you need to buy then is a primer that is designed to go over tiles, glass vinyl ext. This will etch into the glass and allow you to tile to your glass splashback. Speak to someone in the tiling section at your local Bunnings or your local tile store. Don't be stuck with any myth on what sort of tile you should use. Go with what you love and size doesn't matter, it will not affect anything in any way.
As for set out, the best way is to find the centre. Then step out with your tile from either the edge of your tile or centre of your tile and see what cut works best. If you have measured the centre you only have to step out either left or right, not both as the centre measurement will give you equal cuts if that makes any sense. - gippslandhome
Resaflex is the most forgiving tile adhesive you can get. It has the highest tolerance for movement and has the most polymere content in the market. Just make sure to use the correct height for your glue trowel.
Prime X is my go to primer for starting out your wall. Most of the tradies I've dealt with recommend the product. It is DIY friendly and again easy to use. But like any primer, read the instructions at the back so you get the timing for the layout correctly. Too early and the primer will not be hard enough. Especially in this cold weather at the moment. You may have to give it extra time to dry off so that the primer sets and you can then proceed. - redracer01