Not every team has a parent club. There are many kinds. The most common in FM09 are are a bigger club will send you players on loan to get their youngsters more experience. Another kind is that they arrange an annual friendly and you get to keep revenue.
Example: Im Peterborough and I have the option of loaning several W.B.A. players due to them being my parent club. I also arranged a friendly with Celtic annually.
It is noramlly only 2nd tier teams that have parent clubs. To check them go to main team selection screen and click on Affiliated Clubs. It will show Feeder and Parent clubs.
Odds are is they will be lower. Probably teams like Leeds, Forrest, Leicester etc. No offense to your side but the likes of Man Utd and Arsenal are unlikely to sign a club that low as a feeder side.
For Peterborough (League 1) I was given an option of WBA, Birmingham or Forrest. Im sure you will have lower teams again for now until promotion.
Not any. They might offer a list of available players or just make offers on certain ones. I mean if you got Chelsea for example you wouldnt get Drogba, Cole, Lampard but Ferreria, Makelele, Sahar would be more realisitc. You wouldnt pay wages.