Replace rotted wooden sill of the door

I agree with Jeff Widmer -- you don't need a bigger/stronger bracket, as it's not the bracket that failed, but longer screws to properly fasten the bracket.

Given that, your jamb repair doesn't need to be structural so don't sweat how strong it is and just make it look nice with whatever product you've used before and liked. After you drill your pilot holes for the new bracket screws, drill out the repaired jamb with a bit that's larger than the screw threads so the screws don't stress your repair. Of course you want this larger hole to only be the depth of the jamb, maybe 3/4".

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.