Q:
Is there anything to get it working faster? The internet is very slow via the two [not directly] connected computers.
A: That depends, what slows down alot of networks without people realising is while thier HUB is 100Mbit, often is the case they go for cheap network cards that are only 10Mbit. This should still mean you won't see any drop in internet speed though.
A MAJOR factor with networking equippment is making sure to get Full Duplex Hardware. This is extremely important because if your on Half Duplex you card can only do one operation at a time, either receive or send. As such this will bottle neck the entire network... Some cards require you to put them into Full Duplex mode manually, and other cards will do it automatically but this is the biggest speed killer.
As for Linux, well I know that most Knoppix builds will connect seemlessly into Windows ME/2000/XP/2003 Networks Seemlessly and detect on boot. Thing is Linux is fussy, and it doesn't like communicating directly to Broadband Modems without having the registering NIC inside that machine, so while Windows will happily share a modem through a hub, you'll have to setup one of the machines as a network gateway to the internet. Another problem you'll face is you can't use Linux as Windows doesn't like communicating with it.. While it'll share a network if it's in-charge it won't use something Linux is shareing. It's fussy that way really.
