Congratulations on the new TT
There is a post from earlier this spring where someone has the same table design, and added reinforcement. I recall they added the new wood to the outside (visible side of the bench). Then secured the table to it.
If it was me, I would remove the bench top and add a large wood panel spanning a decent area, behind the existing frame (out of sight). Secure that panel to the existing bench frame, maybe to the floor too. Then I would consider drilling through holes for bolts. Paint bolt head black once your happy with the install.
Wire gauge depends on a few things; How far is the outlet to where your plugging in at? Do you plan just to keep it plugged in so you can keep the batteries charged, run a few lights and the frig? Or do you want to run the AC? At minimum you want to use a 12 gauge heavy duty extension cord, and keep the cord as short as reasonably possible. Do not coil up any extra cord, lay it out.
Pressure Regulator; Personally I like to keep it under 45psi, but many people run 55 psi, a few run in the 60's. I would not recommend a set point greater than 65 psi! I do not like over 55 psi, as the pex fitting connectors used in TTs are not the same as what is used in a house and have a greater rate of failures/leaks.
I would also recommend doing a leak test at home. Put some water in the FW tank. Purge all the water lines using the water pump. Turn off all faucets, leave the pump on. If the pump cycles while the faucets are turned off, you have a leak. More frequent the cycling the bigger the leak. I can leave my pump on all night, and it will not cycle.