I feel like you can do both these days, can’t you? Hades was one of the first to break this ground.

Gravity and vacuum are not mutually exclusive - you always have to deal with gravity forces, although they become negligible pretty quickly when you get into and then leave orbits.

As to the specific claim, I suspect that the experiments they are currently doing (in vacuum chambers on earth) have gotten to the point that they are measuring the propulsion system producing more thrust than it’s own weight (T/W >1), which would technically be enough thrust to overcome gravity. Even if it wasn’t practically useful for actually getting to orbit, that amount of thrust on a reactionless motor would be incredible, and would totally unlock the solar system for us.

When you say “university staff”, do you mean professors, or some other technical support staff?

If professors, then reaching out by email is probably a good way to start. They may get a lot of emails though, so your best chance to get a response might be timing the email right at the start of summer when they hopefully don’t have any ongoing classes.

In terms of payment - most professors would happily talk about their areas of study with interested people for a short time (for free). If you needed a significant time investment from them though, then you might start having issues.

In my time looking for published papers, I have only very rarely seen papers which are also hosted by the university of the author. I suspect in your case it was hosted because of something specific to the school or the author, rather than a general thing.

What I am seeing more often in my field is people posting a version of the paper on “arxiv”. This is a similar open-access approach, but you do have to be careful with arxiv papers as you can post anything on it, including work that never was or will be peer-reviewed.