Everbearing raspberries will tell you what to cut because spent canes and parts of canes become visibly discolored and dry.
Normally a fresh cane from the current season will bear fruit and in the next season, you'd normally cut away the top 1/3 or so and the cane will regrow a bit and bear again from the remainder - but again, the dead part will be visible, so 1/3 is not a hard rule.
You can also decide, for example if you have high disease / insect pressure, to cut down canes entirely at the end of season and let the rasps regrow from the ground each year. That's entirely fine with them, it just means that you'll be getting one big harvest later in the year instead of an early wave and a late one.
Speaking of insects, check your canes for visible bumps - balls formed on the canes, usually on the lower half. Cut those canes out entirely and burn them.
For mulch, I very much suggest sawdust, rasps like it a lot. Sprinkle with some (just some!) high-nitrogen whatever if you're worried about decomposition stealing nitrogen from the surface of your soil. And get your sawdust as rough as possible so it doesn't just harden into a solid layer. Whatever you do, do NOT leave soil bare... Rasps are thirsty and have shallow
roots. Keep that moisture in!
Is that
ash on the ground on the pics #4 and #5? If so, that's possibly not a good idea. Ash has an alkali reaction but rasps are acid lovers.
I'm reading your previous topic about the raspberries. Polana is a good choice! Polana and Polka are really robust. But the 16-16-16 that you mentioned is a strong fertilizer and, in my opinion, too high in nitrogen. Rasps don't really need / enjoy lots of nitrogen. Better use an orchard-type fertilizer that has relatively N but high P and K. Of
course if you've done a soil analysis and found out you already have lots os those then... Just don't fertilize and observe how it goes. Also, yes, some shade in the summer is a good idea.