Yes, water is fine as a rinse between dev and fix in this case. 30 seconds is fine.
The time at 70 degF is 8.5 minutes, according to Kodak. The full information is in Tech Pub F-4016, which is on this page:
link. F-4016 applies to all formats of 100TMX, and it has more information than the developing chart on the same page.
The Massive Dev Chart has more information:
http://www.digitaltruth.com/devchart.html
Seven minutes may be too long for fixing, if you use a rapid fixer. I rarely fix T-Max for more than three minutes. Check the clearing time by cutting the leader tongue off the film and dipping it into fix. The fixing time should be two to three times the clearing time. Typical clearing times for fresh rapid fixer are 15 to 30 seconds.
I'd be inclined to wash for more than five minutes if you are using running water. Kodak recommend 30 minutes, or at least six changes of water. I prefer the changes of water approach. It's easier to keep temperatures reasonably even that way. Fill and empty the tank six or seven times, with a minute of agitation between filling and emptying.
Do a 30 second final rinse in distilled or deionised water while the film is still on the reel, shake the water off the reel and dry on the reel or (usually better) off the reel, hanging up in a dust-free area.
Best,
Helen