Haven't got time to do a full reply, but we have 2 DSs, currently 4 and 6, and have had APs for nearly 3 years. We have had 4 really good ones, and 2 duff ones.
We use an agency (same one which specialises in French APs - important because we speak French and so there are no misunderstandings).
We eat with the AP in the evening, and she is free to watch telly, but usually they disappear off to own room. If you don't want them with you, suggest the room is warm, homely, and that you have wifi (most have their own computer).
The room sounds fine. Where we are at the moment, the AP has sink in bedroom, but shares loo/ bathroom with the family. We are moving soon and she will share with boys, while we have an en suite.
Current girl is brilliant with boys, despite her limited English (it is improving), and they have got on really well with 4 of them. The 2 girls that didn't work out lasted 3 and 4 months. to be honest, if you get the impression it is not working, it probably won't improve.
We also have them in full time nursery/ school - be aware that an AP can't have sole charge of an under 3 for more than minimal periods. Also, they do a max of 25/30 hours a week.
Good luck! It works for us, and will have to continue working for another 6-8 years I guess.