I am wondering if it is ethical and acceptable that a Ph.D. student receiving fund and RA from a university and a Prof collaborates on a topic with other researchers and professors (other universities)? In this situation, should we inform our supervisors?
Yes, it's totally ethical and acceptable. Research doesn't happen in a vacuum, and collaborations are generally beneficial to all parties. I cannot imagine any funding body or person preventing you from collaborating with others. Talk to your supervisor first, of course, as they may want to be part of the collaboration too.
Yes it is ethical. Whether it is acceptable will depend on your field, your stipend situation, and your advisor. In all cases you should inform your advisor.
Field-dependence: In some fields (like humanities, possibly mathematics), you are not really using the advisor's physical resources, and the advisor/advisee relationship can be rather distant. In others (like engineering), you need your advisor's lab and experimental platform to conduct research, and the relationship is necessarily much closer. In the latter case, it is more likely that the advisor will place some restrictions on where and how you spend your time. For example, if the external collaboration involves their lab, their equipment, their resources, they are not going to react well to being "cut out of the loop."
Stipend dependence: Your stipend's source is also critically relevant. If you are on a contract PhD stipend, you are funded to perform specific work and you must hew pretty closely to that direction, regardless of the advisor's opinion on the subject. If you are funded directly from an advisor's grant funds, but whose specific research tasks are a bit fluid (the typical case in the US, for example), then your advisor may object to you spending a lot of time pursuing research outside of what their grant funds are paying you to accomplish. If your stipend is fully paid by the university or your own grant, then you are clearly the most free to act how you choose.
Advisor dependence: Some advisors may not pay too much attention to what you do, so long as you finish all the work they assigned you. Others will keep a closer eye on things and would object to you doing any work outside of their laboratory. Still others may be perfectly happy for you to pursue your independent work, but they would still want to advise you and furthermore probably want co-authorship on your eventual publications. However, in every case, I would make sure you discuss your plans, including who you are planning to work with and what you are planning to work on, very clearly with your advisor, so they don't find out after the fact that you just spent the past 5 months working on a dead-end project with their most hated competitor!
Personal perspective: I would most likely object to a student choosing to collaborate outside of my laboratory with no involvement whatsoever from me. My thinking is as follows: when I take a student on, I am making a commitment to them to train them to the best of my ability, and to usher them safely (as safe as possible, anyways) from the starting line to their successful PhD defense. As part of that, I would want a "sign-off" at the very least of any project a student took on, if for no other reason than to make sure the student wasn't wasting their time or getting involved in a project I didn't think was going to come to a good outcome. Then, if I approved, I'd want to be involved in the project going forward for the same reason, to continue to give my advice and keep the student moving productively forward towards their final defense. If they don't want my active mentorship, they should switch advisors! Of course, as a student gets closer to graduation, they'll get more and more leeway with me to do whatever they want to help foster their independence, but I'd still want to be kept informed at the very least.