Softspot are exactly that. If you press on them, the bend much more easily than other areas. If you tap them with a screw driver handle, they make a hollow "thud" sound rather than a crisp knock sound. They are common in front of the tramp for sure. If it has been sitting on the ground a long time, you may want to look for blisters etc around the bottom of the amas.
You won't really know what you have until you get it on a trailer and hit it with a pressure washer. Then if there is damage you can see it better.
As for the trailer. As insane as this sounds, it really depends where you live and how you intend to use the boat. Here in Georgia, it is not remotely uncommon to see trailers that have not been registered for a decade in land slips around the lakes. They rarely leave the lake area so no one registers them. I am certain the lights don't work etc. Note I say rarely, not never. Personally, I would get it in working order, properly tagged etc because, with my luck, if it were not, I would get into some sort of mishap on the road and have a massive headache

....
Take this with a grain of salt but ...... When I went to register my hobie trailer this year, the sheriff had to come out because there was no serial number plate on the trailer so I had to get him to certify such so I could get a new serial number from the DMV. No joke, he asked me why I was bothering to go through such aggravation for a small trailer "Nobody's gonna bother you pulling a boat around as long as the boat is registered" I did not take his advice, it is properly tagged and registered it as I planned to take it it other states but.........
Those sails look trashed, you should look around for another set and expect to replace all the running rigging.
Good luck with it. I just picked up an older 16 fairly cheap (good trailer, good tramp, and a few soft spots) and am getting ready to repaint etc.
The beauty of these forums is that you can get a lot of information, you just have to sort through what is information versus what is fact

I personally have had excellent experience from West Marine swagged standing rigging on a wide variety of boats (FDs, Lightnings, NZ Javelins, Ranger, Coronado) and never had a problem - the FD and Lightning probably being the closest comparable here - although I would never accuse West of being "cheap" at least not on a cost perspective. With that said, I am brand new to hobies so there may be something inherent to their rigging I don't know which would cause a problem????
With all that said, in my 35+ years of sailing, the only time I have seen standing rigging fail is if it was neglected/not properly maintained or an error was made during stepping (much more common on trailered sailboats).