Do I need to login/maintain an account on these other machines?
No, just once to activate Steam Guard on their machine
If someone is playing a shared game do I get locked out of my game library until they are done?
No, they will be kicked out of their game to allow you to play. Per Steam Family Sharing FAQ:
When I authorize a device to lend my library to others, do I limit my own ability to access and play my games?
As the account holder, you may always access and play your games at any time. If you decide to start playing when another user is already playing one of your games, he/she will be given a few minutes to either purchase the game or quit playing.
Clarifying for @WernerCD - any game activated on Steam will kick the person with whom the library is shared.
If they do something stupid like obtain a VAC ban am I subject to the same punishment?
Yes, your account might get banned for any cheating/fraud conducted by the one you share your library to. Per Steam Family Sharing FAQ:
Will I be punished for any cheating or fraud conducted by other users while playing my games?
Your Family Library Sharing privileges may be revoked and your account may also be VAC banned if your library is used by others to conduct cheating or fraud. Additionally, VAC-banned games cannot be shared. We recommend you only authorize familiar computers you know to be secure. And as always, never give your password to anyone.
Are there any (other?) disadvantages to myself if I share my games?
Not really, only disadvantages are on the other side (limited availability when the library owner is playing, no offline mode to play shared games, no trading cards gathering, etc.)
Steam Family Sharing FAQ can be found here.
Best Answer
As per the Family Sharing FAQ:
A game might not be available for sharing due to several reasons.
A little more info can be found here:
Additionally, as stated here, "PC versions of Activision games will only be playable in the region in which they were purchased". Since the region you're playing in is checked through your IP address, using a VPN can also restrict your access.