I had to take a break from researching all the rules, regulation, codes and requirements. It was melting my brain.
From what I have learned, you will almost certainly need a few permits. Even if it is just a few panels on the roof of a shed. this is because it is a permanent installation. (And if you really want to try and follow the laws too...)
For the shed, if it is a premade metal shed, you will probably have problems. For the mounting of the panels, you need to show roof loading. This is to show that the roof can support the weight of the panels. If the shed was built with traditional building methods like wood or masonry and has a truss or rafter style roof then you might be able to get somewhere. You just make a little plan-view drawing, show the roof loading in a note on the drawing, show a manual/cut sheet for the mounting brackets you will use, show the cut-sheet and UL/CEC sheet for the panels Show all that to you local permit office and see what happens.
The you need electrical permits for connecting the cable from the panels to a junction box, fuse, breaker, etc. That is pretty easy stuff. You should be able to get a permit as a owner-builder for that as well similar to the above building permit.
Now converting the DC electric from the panels to AC is a fishy area. I 'think' if you stop permitting at the DC point of connection from the panel, just set a little 1000w inverter on a work bench and plug in some tools than no one can really do anything to you. Or you could get an off the shelf battery box/inverter/solar generator backup and just charge it from your panels.
Honesty though, for you situation, just make a non-permanently mounted setup. Maybe just lean the panels up against a wall where you can easily just pick them up and put them away. Or just slap them on the shed and not worry. If then man comes and says to take them down, it is really not much liability to you. Just say "ok" give a thumbs up and take them down.