From what little I know, RA and RO differs in the requirements to qualify for it. RA does not require a degree, so a student, especially those carrying out their FYP, can be hired as RA. Once, you have a degree, then you can be hired as a RO. Another notable difference is RA does not have EPF and SOCSO, and allowance claims are made based on maximum 12 days a month as Mr. Botz mentioned. For RO, you have a regular monthly allowance, EPF and SOCSO. Someone please correct me if I'm wrong.
On top of that, I think there is also a Research Scholar these days, whereby as the name implies, it involves obtaining a scholarship from external companies.
Also, even if you are hired as an RA/RO, you can still apply for mybrain15. If you are lucky you will get it as well.

Mybrain15 covers only the tuition fees, does not include library fees, IT fees etc. As far as I know, MOHE deals directly with MMU, MOHE will be informed on how much to pay, and then they will pay directly to MMU.
About the funding for research projects, I'm not sure, but I believe usually these stuff are handled by your supervisor/lecturers? I believe lecturers usually try to get funding from various organisations for research projects of their interests, and once they obtain the funding, they can usually hire a RA/RO/GRA to carry out the project. I think so la...

Bare in mind though, usually funding comes with requirements such as publication of papers/journals at the end of your research.