1: Correct, entering a host is not a dice test, so there is no penalty.
1a: There are no devices in hosts. A host contains only files and personas. Devices slaved to a host can be accessed from within as though you had a direct connection to them, therefore there are no noise penalties
1b: Correct: It's the trade off of having a possibly very strong master lock, but once you have cracked it you have full access to all it protected. That said, the new Kill Code book introduced a new type of host (Industry) that no longer grants the direct connection benefit
2: Yes, you can switch to AR as long as you are not link locked. Moving around the real world is possible but doesn't mean you move through the host - and vice versa.
2a: AR has nothing to do with how easy you are to detect. AR just means you have a dp penalty and rely on your RL ini to act (and you don't take biofeedback damage which can be a very substantial benefit)
3: If you run silent you have a -2 penalty. You can forgoe running silent but that makes it pretty trivial for anyone looking for a hacker to check your device for illegal matrix actions. So as long as no-one notices you using sleaze actions, you don't have to run silent to hack.
3a: Provided you modified your Persona to look like it belongs to the host and you never fail a sleaze action you should be fine. That said: Some hosts have their patrol ic set to be paranoid and may be scanning any persona they detect for illegal matrix actions. In that case it would be better to work in hidden mode
4: Yes, you can communicate pretty freely even while inside a host. That allows leadership and teamwork actions up to a certain degree. That said, you can't watch someone in the matrix if you aren't in the same host as they. A persona that enters a host vanishes from the matrix.