You're underpriced. To find out what price range you should be at just take your KCS divided by 2. For example, a 500KCS person would cost around 250B. Of course people like to overprice specific, active tuts so price ranges will vary.
I don't know all of them, but here are some of them: My pupil Bluntwiches Riccena Lillie (the username is something about abduction and aliens) Ahli (I think it's Ahli-LovesMike but im not 100% sure) Flumsy (or is it flumzy?) And im not sure about the rest. I believe there is a total of 12 though
I don't think tutors affect jobs. Tutors are for max plunder (15m x kcs) and provides tutor bonus to hit and defend battles. Maybe it does slightly affect? I think it's just stats because as you upgrade more, most jobs will get easier. Just don't hit from almost dtw as jobs are harder when you're weaker. You'll finish that job in time. Good luck!
6 parties to unlock Cat Cafe. Draw Magna! A 2 hour party. Noodle Express. A 3 hour party. Enjoi J-POP! A 4 hour party. Cosplay Please. A 4 hour party. Anime Expo. A 5 hour party. Big in Japan. A 5 hour party. Then you will need a Hypnocat which costs 79 extra credits to hit Cat Cafe. A Hypnocat can be bought via the store.