I want to play some of the Steam dating sims, but I don't want to get derisive messages from my Steam friends when they see messages like "Nzall has started playing Tank Dating Simulator". Do the Steam rules allow me to create a second Steam account that I can play games on I'd rather not announce to my friends that I own them?
Yes, it does. There isn't anything in the Subscriber Agreement against it.
In fact, you can use the same mobile phone number on multiple steam accounts too.
Also it is clearly stated that you can (and recommended to if you are setting up a dedicated server) create another account:
For security reasons it is recommended that you create a new Steam account just for your dedicated servers.
It is allowed, but it might not be necessary. You can manually add the game's executable as a non-steam game, and name it whatever you want.
This way, it never shows on your public profile: non-Steam games don't have hours tracked, neither show up on the recently played section of the profile page. The only place it will show up is if one of your friends goes to that specific game's store page, you will be in the "Friends who own this game" section.
For more information, see this page.
It is allowed but not necessary. On your friends list click the arrow next to your name and select offline mode. Then your friends can't see your activity until you sign back into online mode.