2) The way you do things know is go to places and use the PATS app to click on the characters at the top right of the screen. Specific events will lead you to be able to get some items (like the lake water), for others you'll need to buy them from the shops (like cum).
2b) Go inside the gym. Talking to people there will let you train. As for the note, yeah, that's how it is.
3) If you go to bed, you'll wake up at 6 AM and can do the Morning/Afternoon events. Staying part 7-8 PM will make you pass-out and you can do the Night/Early Morning events. As for the money, the farther away you're from your Home when you pass out, the more money you lose.