Shower – How should I apply silicone sealing to shower screen glass

This is a tough one. There is no easy way to remedy your problem. The best way would be to remove and replace the tiles properly. If in fact the tiles are real marble, you can grind them to create the proper angle and slowly refinish the surface by stepping down grits and finally getting to a wet polish grit of 2400. That is actually impracticable for a DIY if you don't have the equipment and materials to do it. If it were me, I'd remove a couple of tiles and reset them to fix your drainage problem. A couple of hacks with a hammer, scrape off some of the thinset, replace the tiles with a little premix thinset, regrout, wait a couple of days, seal the grout and your done. The actual labor time may be only a couple of hours, even though you have to wait a bit to use the shower again.

It does not appear structural, as the seat itself is still flush to the wall. If the seat were failing the seat top would be pulling away as well.

My guess is that the panel in question was installed with a slight angle there - poor cut or something - and that the caulk used has just given up, as caulk does. However, more camera angles showing the seat would help confirm that suspicion.

As for do you need to dry it - as long as there is only marble back there, no, water won't hurt marble. The problem is, you can't actually tell without pulling it apart. If there is any wood there, however, I'll be very surprised.