Can multiple computers install to the same shared SteamApps folder?

For each installation of Steam, you can add your SteamApps folder from your drive from the settings. (Settings > Downloads > Steam Library Folders - See image)

As long as the SteamApps folder layout is the same for all systems you'll be using, there will be no problems with installation. Possible problems with this include savegames inside the game folders, patching from multiple computers at the same time and that installing and deleting games requires you to restart Steam on other computers.

Note that only games that use the new content management support this. This includes most modern AAA-titles and almost, if not all recent releases.

This sounds like a horrible idea. Your game load times will suffer immensely, since all of those gigabytes will need to be read to your computer over the network. Additionally, I doubt very much that Steam has any support for this at all, and conflicting updates and installations will likely corrupt your games. If two or more people are attempting to play games off of it, you will probably run into more issues.

If space is an issue, getting a good external hard drive with USB 3.0 or an eSATA connection will give you lots of room with plenty of space and no speed compromise.

You can forcefully redirect one folder to go look for files in another place using Junctions...This is an application that should simplify the process however you can make junction on your own in CMD without having to use this application,but it is kinda hard to find good guide.

It looks like there are a lot of things that can go wrong with this,but if you only share "steamapps"(data) folder,and keep 2 separate installations of steam with their own personal files like settings and saves and have very good network connection you might just pull it off.

Considering updates while both parties use the same steamapps,if someone is playing and other one is trying to update the game...The other one should fail updating since windows usually don't allow changing files while they are in use.

Also you can't use same files between different OS since their binaries should be different.