I like start.me. It isn't something to download but it's a web page. The free service is a great start. I've been using it for years now
I recently found ground.news. it is an interesting news aggregator sight in that it combined multiple sources for each story. It doesn't really answer some of your needs but for each story it shows you which sources are pay-walled and which ones aren't.
I like #newsblur too. I have paid for it for years now (though it is free).
What I like best about it is that it caches the text and images of the site so I don't get all the ads etc.
Every year or so I go around looking at others but always go back.
I think my first experience was around 1993 or 1994. I downloaded the 3.5" disks at the university and then uploaded onto my 386. No GUI, all command prompt. :).
Right around that time, too, I found some network cards and co-axial cables and 3-4 of us in the house put the cards in our computers and could see each other's computer. Couldn't do much else though. Hahahaha.
I purchased sync. I agree it is a little on the expensive side.
The one thing you can do is just use git and turn on the push and pull. It seems to be very reliable this way. Though you won't be able to use it on the phone as far as I have been able to figure out.
At least on the Mac (bsdtar) you can extract single files out of a tar file.
E.g.,
Create the tar file:
tar cvzf pseudo.tgz pseudo/
Move to another directory
cd /tmp/tt
Extract a single file:
tar -xf ../pseudo.tgz pseudo/10481_2017.1069.png
You say PC, so might want to check the tar version you are using and see if there are extra parameters to do the file extraction.
That is a very interesting site. I am in the US (but Canadian) and it is helpful to see how the smoke curls towards my area.
I wish there something like that for RSS feeds. That would be fantastic.
For news specifically, Google News and Ground.news both aggregate and cluster similar news articles.