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This is my first visit to Tech Survivors and I have a difficult question (I think).
Welcome, Albert. 
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High speed internet is being wired in our neighborhood via the local cable provider. Now I must decide how to connect all of our computers.
(1) New Powerbook 17” 1.33GH with Airport Extreme. (2) Dual 500MH G4 tower. (3) 8500 180MH tower and (4) New custom built Win machine running XP Pro.
I was interested in Apple Airport Extreme but heard that wireless cards are not compatible with Mac 8500 180. This old Mac has been fitted with an aftermarket USB card but USB wireless requires OS X to operate (right?) and this old 8500 Mac won’t operate in OSX.
Computer (2), the Dual 500 G4 has two hard drives. One is exclusive OS 9.1, the other hard drive is Jaguar. I need to access the internet from both hard drives in addition to the other Macintosh and Win machines.
You can still run wireless. You'll have to cable the 8500 unless you can find an external USB wireless adapter that will run on 9.x, but I don't know of any right off hand (course that doesn't mean much, cause I don't mess much with wireless).
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Is this possible without running Cat 5 hard wire?
See above. 
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Separate question on same issue, will the cable providers maximum speed be achieved using this system or will it require hard wire to prevent loss of performance?
It depends on what your definition of "maximum speed achieved" would be. If you're asking if your cable provider (whom you haven't given a clue as to who it is) is going to open the pipe full out to you on a basic plan, I can tell you that I haven't heard of any that do on the basic plan, but then again, I don't mess with cable either. I'm on DSL. 
I can only give you the testimony that I hear of from the cable subscribers in the town I work in and in Kansas City here. In KC, RoadRunner screams, but the residential still isn't tacked out. In the town I work in, cable is slow to a crawl. It's really bad at this point, but they're working to improve it. Comcast is also here in the area of the city I'm in, and I've heard recently that after some differing reports, that they have got it together and are running much more inline with RoadRunner's offerings. Again, I don't know what YOUR expectation of it is, though. I mean, unless you're downloading 600+MB ISO files on a routine basis, is it really a large issue? I talked with a gentleman with one of the ISPs here in KC today and he showed me a graph of an organization that frequents the 'net and currently subscribes to an ADSL connection with 256 upstream and 768 down. Their usage was at about 5% bandwidth with a LARGE number of users, so you'll probably be good to go with cable. 
Hope that helps.
Take care,
Chris