1) Appointments (new & cancellations) get released 42 days in advance at around midnight. As there is a very high demand for these, they disappear quite quickly. In addition to this the UKBA appointment booking system is rather primitive, by that I mean it throws error messages quite frequently & also doesn't lock a timeslot until you actually fill your details and submit the form. So it is literally a race against anyone else who has logged in at the same time as you & who may have also selected the same timeslot. The person who submits first, wins!
So what you'd have to do is first decide the appointment date you want, then count 42 days backwards from that date, then login a few minutes before midnight on the day with everything ready to book your appointment. Hopefully you'll find one... User experiences are mixed on this forum... So I think luck comes to play here as well.
2) I've not personally used this, so will leave this one for someone else to comment on.
3) Yes, there is such a thing... While the price does sound exorbitant, from what I gather some have made it work, by gathering a group of 10 people to apply at a single location on a agreed day. The reason being that the £6000 premium can be split amongst a maximum group of 10 applicants.
http://www.ukba.homeoffice.gov.uk/about ... r-premium/