1) Yes, those players are from bot teams and we call them nordgen (nordeus generated). The most expensive and young ones (18-21 y.o.) are the faster 5* trainers of the game.
From the market you can buy 3* - 4* - 5* players.
So, a manager from one or two levels above, also can bid for those players but for him (let's say one lv above), it's 3* and 4* so they 're not so attractive if he wants to build a 5* team.
When I move forward in an auction with a manager above me, I 'm happy because I believe he 'll not go so far (to spend so many token I mean) for a 4* player.
That's the general idea of course. There are some exceptions.
2) You can't see you're players in transfer market. Neither in negotiation list.
The second one is a little tricky as if some player isn't very attractive (let's say a MC, 27 y.o., without any sa), you may not have any offer for him for a long time (specially if it's not the beginning of the season).
3) Yes, you can make an offer to a friend from above level, but only for his 5* players (remember also that your friend must be in the same server with you and probably not a fb friend. In that case, you can't see the "offer" button.
6* players you can buy only from the scout list or the random recommended players.