Yes, if you take joint apart clean clean and clean fitting and pipe, flux and re solder
The kit has two parts: Flux Paste and Solder Wire. Solder Wire can be used on stainless steel, but flux paste is not. You need stainless steel solder flux, which HD does not carry.
Flux is used to keep CLEAN materials CLEAN while soldering / brazing. Haven't tried it, but I don't see why it be a problem. Acid flux helps to clean surfaces while soldering- with all of the associated cleanup and fumes! Use caution with acid flux. This flux is water based and has a very low fume level.
Yes, probably but most people use rosin core solder for silversmithing
No, you need a coupling, brace or new pipe section to repair that. But this kit can help you install it.