Without any doubt, use a blowtorch.  You want a fairly small one, and the kind sometimes sold for cooks to use would be ideal.

The problem with silver solder is that the joint has to be heated to red heat, thus destroying the temper of the spring steel typebar and potentially weakening it.  If the type slug has slipped slightly during the process, it would be difficult to undo the joint and do it all over again.  A soft-soldered joint is slightly elastic, thus acting as a shock absorber when the typeface hits the paper.  A hard-soldered (silver solder joint) is not.  Possibly you could use lead-free solder (tin), but I do not know if it has the same elasticity.  Also, it does not have the same plasticity/temperature range as lead-based solder so may be more difficult to work with in this application.  Finally, regarding lead being a poisonous metal - yes it is, but in the very small amounts being used it is hardly likely to cause you any problems.  After all, until about ten years ago all the copper drinking water pipes in British homes were soldered together with tin/lead, and most still are.  I don't think anyone ever died from it !

Something to remember with noiseless typewriters of all kinds is that they are low-impact machines.  Back in the day, you could obtain special heavily-inked ribbons for noiseless typewriters.  Of course, nowadays you cannot.  But ribbons for mechanical adding machines and calculators are heavily-inked, so I would suggest trying some adding machine fabric in your noiseless to see if it helps.  If not, well it has only cost you the price of a ribbon.

Unfortunately your photos do not show up on my computer, but I can speak in general terms.  This is a common problem with this model and one of the first things to wear and go out of adjustment.  When worn, it can be very difficult indeed to set up.  As the carriage nears the RH margin, a ramp on the margin stop should contact the stop and first ring the bell, then a few spaces further on, lock the keyboard.  The stop can sometimes wear out of adjustment so that it doesn't contact the ramp properly.  With care, the stop can be bent downwards to get more contact.  It doesn't look as if it will bend, but it is made of softer metal than it appears.  Be careful with it though.

I cannot imagine that WD-40 would do any more than make an already shiny and slippery platen even more shiny and slippery.  Be aware that there is a lot of nonsense about typewriters on the internet !