For the 3rd, usually you flip the order (same as skipping the の). So 大学芋アイス could read as “University’s Potato Ice(cream)” while 芋大学アイス reads (Potato University’s Ice(cream)"

Funnily enough, most of them are on itch.io. The keyword is furry visual novel (fvn), 90% of which are gay.

The one from the screen shot is Burrows by Nikko. A good pick and an inspiration for the above is Echo by the Echo Project