To answer number 1:
If you delete all those packages you will have to republish them if a client needs them. First off, plan on 150 GBs or so of disk space for updates. You can go to all updates and sort by supercedence. Delete any superceded third party and decline any microsoft updates. Also make sure you scroll down to delete and decline superceded AND superceeding updates as well.
For number 2, number 1 also kind of answers that. You can do the cleanup wizard as well though if you want
For number 3. There is no way to automate all of those. Certain vendors like Adobe REQUIRE users to register every year as a distributor and Solarwinds just cant legally put them out like that AFAIK.
If you are downloading every package from all the catalogs then no wonder you are running out of space. Only sync content that exists in your environement. Watch the new update notification and then go to the specific folder and publish the newest one there, ie. if a Chrome update comes out then go to the Google folder and publish the newest chrome updates. Then go to the next folder, ie Java or whichever and do the same thing. Going to all packages is just a horrible load time and a waste.
I dont have experience with multiple WSUS environments but yes I assume that is what you have to do unless they are replica servers and then it should just replicate updates and approvals downstream.
And for the last one, again, dont click all packages, go to the individual folders.
To number 1:
The picture shows the updates on WSUS and not on solarwinds server written in my question. On my WSUS servers the Cleanup Wizzard runs one time a month. But to question 2 not all updates (especially the old third party packages) are cleaned/removed (also if they are declined and expired).
To number 3:
I don't download packages automatically from catalogs and sync only catalogs which contain products we use. I download and publish packages if I need them (3rd party). Microsoft Updates are configured to download after approval.
The last one is only a try to use solarwinds faster. Only in view "All packages" I can mark all new packages and download or publish multiple packages of different publishers in one step. At the individual folders (per publisher) I have to do download and publish the single packages in single views one by one - this is not very productive too.
That picture is from Solarwinds Patch Manager and is showing both Microsoft and Third Party updates. Like i said, you can sort by supersecedence and then delete any unneeded packages.
Going to all packages may seem faster but in my experience its not. I guess you will have to play around and see what works for you. It sounds like you already have a method you like so just keep doing it.