1. Are you talking about Dream Club: Host Girls on Stage for PS4? If so, it's a free download and only available on the Japanese PlayStation Store.
2. Not too many you can't get in the U.S. or European stores, but there are a few. You can browse them all
here. But here are some standouts: Yakuza: Ishin, Puyopuyo Tetris, Fairy Fencer F, Tears to Tiara II. For some reason, a lot of demos, like Yakuza 5 or E.X. Troopers, are removed after a while.
3. Yakuza: Ishin demo is already out on the PS3 PlayStation Network. The PS4 demo should be live by 10 a.m. EST tomorrow morning. I'm assuming (due to Japanese launch). The page for the demo is there on PS4, it just doesn't allow you to download anything yet.
I should also note, on the Japanese PlayStation Store via PS4, you can get three free months of PlayStation Plus, giving you access to a ton of free Japanese PS3 and PS Vita games.You can find a list of stuff
here. Notable standouts: Dream Club! Complete Edipyon, Ciel no Surge, Demon Gaze, etc. Just today, they added the
five hour full-game trial for Ar no Surge. Which is cool, because it's not out yet.
I think it looks quite good.