I have the following schedule:

London - Madrid, arrive in 4S at 23:05
Madrid - Buenos Aires, depart from 4S at 08:45


Considering the relatively short wait between flights (< 10 hours) I'd rather stay in the terminal than go out. I have access to the Iberia lounges so I'll just try to get some sleep and then use the facilities at 6AM when they open up. Going out means doing passport control twice and what is worse, doing security in the morning. I'd be reaching at hotel after midnight only to be back at the airport for about 6:30. I have seen the air rooms in T4 but at 180 euros I'm not sure it'll be worth it.

Questions I have though:

1. Will the luggage go straight from London to Buenos Aires or do I need to collect it in Barajas?
2. Will I be allowed to stay at the terminal or will there be an issue?
3. Any other tips or thoughts are appreciated!

Thanks!