Successful soldering (you're not welding, and you have the wrong torch if you want to weld) requires that the work be physically clean (scrub it) and chemically clean (flux) - you need a very aggressive flux for stainless, because the reason it IS "stainless" is that it forms a strong oxide layer which protects it from most corrosion. Kester is not going to regard stainless as electrical work, for one thing, so don't bark up that tree too long.
With thin stainless, the other problem you almost certainly have (stainless conducts heat poorly, which makes it very easy to overheat) is overheating the work - once work has been overheated, you have to return to physically cleaning it and refluxing before you have a hope in heck of getting solder on it. You also need to stay out of the "oxidizing cone" of the torch flame - ideally, switch to an oxy-acetlyene torch, make the flame rich, and only use the feather - but you can get there with propane if you're careful. The thickness of the solder does not matter much - you heat the wires, and melt the solder on the wires - don't heat the solder.
You could also move up to brazing, which is a process similar to soldering but at higher temperatures, using different filler metals. When most folks refer to silver soldering, what they actually mean is silver brazing (the rod has some silver, but not a huge amount.) The solder you linked to is a low-temperature solder that has silver in it, from the "lead free" change in "soft solders."
What this is doing on a DIY home improvement site is another question. High voltage electrical projects are not exactly the bread and butter of DIY. Another approach in a lab setting would be to do the whole job in a glovebox full of nitrogen or argon. You could also TIG weld it, if you were good at TIG welding. Spot welding might be another approach, but that will also work better on stainless in an oxygen-free atmosphere (glovebox, etc.)
I agree with lowercaset's answer: No-hub coupling is the way to go. To answer your followup question:
While different pipe materials will have the same nominal pipe size, they will have different actual outside diameters. When selecting a no-hub coupling to join dissimilar pipes, you need to select one with the correct ends for the two pipes that you are connecting.
When you look at the website for the por-flex couplings, you'll see a list of models and what their connection combinations are. You need to pick one that matches what your connecting.
As for the corrugated coupling in your post, that looks like a typical coupling used for joining cast iron.
The other option that you have is to remove all of the copper/brass right back to the hub of the cast iron. Then you can connect the PVC to the cast iron hub by the use of a rubber donut.
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The main problem, if any, assuming the solder band is complete and without flaws or gaps is if there's too much solder on the pipe and you cannot insert it into the fitting. The pipe is "tinned" or coated with solder, and there's nothing wrong with that.
The usual approach to making sure that the coating is thin enough is to wipe it down (while the solder is molten) with a rag - easiest if done when you heat it up to take it apart, but you can heat it up again and do that if the fitting won't seat properly as it is. That should leave it thin and nearly mirror-shiny, which is what you want. Caution is needed as you are dealing with hot, molten metal.
The basic secrets of soldering are that things should be physically clean (shiny metal) chemically clean (use appropriate flux) and not overheated (too much heat burns off the flux and solder won't wet the newly-oxidized surfaces.) The silvery solder is perfectly fine shiny metal. Dull gray solder needs to be cleaned up, but there's no need to go to copper.