[Trippynet]

1) Octane is a faster and more capable system than Indigo2, and might be a better starter system in my opinion. I love Indigo2s, but they are more limited when it comes to performance. Plus graphics options for Octane are much better - kind of obvious really as Octane was the successor to Indigo2.
2) No. YouTube needs a pretty modern browser supporting HTML5 for video playback. The newest we have is Firefox 3, that won't handle YouTube.
3) It is possible to install some flavours of Linux, however GUI support on V8/V10 does not exist as far as I know, so you'll be stuck with a command line. And to be honest, it's a complete waste to use Linux on an SGI machine IMO.
4) Not natively, no. Saying that, you could hook an SGI machine up to a wireless repeater or something to work around this. In my man-cave, my PC, NUC and SGIs all connect to a switch which is cabled to a wireless repeater that hooks onto the wifi in my house. This works fine and means I don't need my machines physically cabling into my broadband router.

Regarding monitors, you could use a standard PC monitor - but it must support Sync on Green, or else you'll get a display with a very green tint to it. Alternatively there are some adaptors that will supposedly allow a none-SOG monitor to be used, but I haven't used these myself. Note that graphics output from the Octane is 13W3, so you'll need a 13W3 to VGA adapter (one that is SGI compatible).

For the SGI 1600, those graphics cards are for PCs - they won't work in an Octane. I believe it is possible to run a 1600SW on an Octane, but it isn't trivial, and to be honest I'd wait for someone who knows more here to confirm.

Final point, I would strongly advise against considering any real form of modern web browsing on an SGI machine. They're simply too old for it, and modern browsers are an absolute nightmare to port (hence Firefox 3 is the latest we have - and even then it is very slow). You're far better off using rdesktop to remote to a PC or something and browse that way, or browse properly on a PC and use your SGI for other purposes.