Use the diagram I made except that instead of wiring to the driver switch you use a momentary toggle switch that you can install in the dash to manually control the mirrors. See attached picture.
To answer your questions if your existing mirrors do not have the perimeter lighting or the blind spot indicator then the wiring in the truck to the mirror connector will not have the necessary wires to make the functions work even if you buy a mirror with those functions available. This is why all the wiring in my sketch is new.
For question 1 the mirrors will work with the key fob, also with the door lock push buttons on the exterior of every door except the driver door you have to push twice and with the lock and unlock buttons inside the truck.
For question 2 yes all the other functions such as the mirror adjustment and mirror heating will work since your truck already has those functions.
Here are the parts you need:
Mirrors (eBay AM-Autoparts)
Side View Mirror Heated Perimeter Light Power Folding RH for Silverado 1500 item #374894886663
Side View Mirror Heated Perimeter Light Power Folding LH for Silverado 1500 item #374994048223
Momentary toggle switch (Amazon - TWTADE / 4Pcs Momentary Boat Rocker Switch 3 Pin 3 Position(ON)-Off-(ON) SPDT Mini Car Auto Boat Round Rocker Toggle Switch 6A 250VAC/10A 125VAC KCD1-5-12)
20’ of 18 AWG 2,4 or 6 conductor wire (2 conductor for the power fold, 6 conductor for adding the bubble light and the work lights)
Power fold mirror controller (Amazon - Tbest Auto Folding Mirror Module,Mirror Closer Modules Folding Closer Module Universal Replacement for 12V Car)