Apple: Airport extreme, 3 questions
Solution 1:
The AirPort Extreme serves your files via AFP and SMB (Mac and Windows file sharing, respectively). I'm not aware of any alternative OSes that can be installed on the base station.
The AirPort Extreme is completely silent. It seems to be convection cooled. I don't think it even has a fan, but maybe it does for when it's running in hotter environments. Your hard disk will certainly be the bigger concern, noise-wise.
Yes, the AirPort Extreme can do the same things the Time Capsule can do with respect to joining and extending networks.