I can't find any sources that corroborate, confirm, or falsify the article, so I'm going to treat it as if it was accurate, in order to answer the question. That said, given some of the articles (complete with an obscenity or two) that popped up when I first saw the site, I wouldn't exactly cite this thing in a publication, report, essay, paper, . . . You get the idea.
Would this violate the OST? (Bullet #3)
There's good news here, and then there's bad news. The good news is that the project would not violate the OST (see http://history.nasa.gov/1967treaty.html for a detailed transcript). The treaty does not prohibit peaceful detonations; however, it does prohibit detonations of weapons (see Article IV). Great, right? In fact, the program wouldn't even detonate anything (at least, not on purpose) - it would use a nuclear reactor. So the OST would be non-applicable because no detonations would be taking place. The program should be fine.
We've been putting nuclear-related power sources (well, primarily RTGs - radioisotope thermoelectric generators) in space for quite some time. They are an excellent source of power for satellites and unmanned spacecraft - such as the Pioneer probes. There shouldn't be any opposition, given the success of these devices. The big differences are that most previous nuclear devices were RTGs, not nuclear rectors, and only provided electrical power to the spacecraft - the nuclear reactor one proposed would power the engine.
Notice that I said unmanned. There are quite a few concerns about humans and nuclear-powered craft - after all, how many people do you know that would enjoy spending months 50 feet from a nuclear reactor? Health problems are, or course, on the top of the list, and an emergency - think a mini-meltdown - could be un-fixable.
I think that the reasons outlined above would make any modifications to the treaty unnecessary (Bullet #2). That is, as long as the rockets kept on using nuclear reactors. You may have heard of Project Orion - the crazy idea to power a spacecraft via "nuclear pulses" (dropping mini nuclear bombs out the back). Well, aside from the obvious health risks, there is another issue with this type of propulsion. The OST? Hardly. It allows for peaceful detonations. Such a rocket would, however, violate a little something called the Partial Nuclear Test Ban Treaty of 1963 (also called the Limited Test Ban Treaty, as well as a dozen or so other names), which makes any detonations aboveground (and thus in the atmosphere or outer space) illegal. So should an international consortium decide to, for some reason, go in that direction, then the PNTBT would need to be modified. Fortunately, it doesn't seem that the project is going, or ever will go, in that direction.
Like I said before, the only part of your question I can't answer is the first part (Bullet #1). There is a brief mention of something on the Wikipedia page for Nuclear Thermal Rockets, but I can't find anything else (its source is here: http://www.space-travel.com/reports/NASA_Researchers_Studying_Advanced_Nuclear_Rocket_Technologies_999.html).
I hope this helps.
You can find a transcript of the PNTBT at http://www.state.gov/t/isn/4797.htm.