The only difference is that Safe-Flo is the retail branded version.
No. Oatey does not manufacture a solder or flux for this application.
Yes. Flux is designed as an oxidation remover and actually etches the pipe in preparation for the soldering process to be successful. This is why it is important to flush the lines when not using water soluble fluxes. Wipe excess flux off the exterior of the pipe after solder joint has been completed, and never wait more than four hours to solder a joint after applying any flux to the joint.
You will start off by getting a five gallon bucket and small electric pump with two washing machine hoses. Mix 1-one pound box of TSP (Tri-Sodium Phosphate), 16 ounces (2 cups) of bleach and hot water in the five gallon bucket. Drain enough water from your system to allow this mixture to be pumped into the water lines, and circulate throughout the system for one hour. The best location for hose connections is the hot and cold washing machine valves. Drain the system completely and repeat this process again. After the second application, you will want to flush the system out through each fixture for at least 15 minutes.  
The water soluble flux is less corrosive, and self-cleans on the interior of the pipe as water flows through the lines. The water soluble flux has a narrower temperature range when heating, but it works with all the solders. 
None. Oatey does not manufacture a solder or flux for this application.
None. Oatey does not manufacture a solder or flux for this application.
Oatey 95/5 Lead Free Acid Core Wire Solder, or Oatey Acid Core Wire Solder.
Oatey 95/5 Lead free Rosin Core Wire Solder, or Oatey Rosin Core Wire Solder.
It is important that you never flux a pipe that will not be soldered within a 4 hour period of time. Flux is an acid and will have an etching affect if left on the pipe to long without heat and solder being applied.