Obviously, nothing on the internet is ever 100% safe. If you're unwilling to accept any risk, you should never even connect your computer to any network.
That said, I think the fact that an .edu domain is controlled by a legitimate educational institution
does make it safer, because such institutions generally have strong policies about what types of files users may host on their network, and strong penalties for users who violate these policies. A .com domain might be hosted by a provider who has similar policies, or it might be hosted by a "rogue" provider in Russia or China who doesn't care what's on their servers.
Finally, I've been using the internet on a near-daily basis for the last 15 years or so, and have never -- not once -- had my computer infected with any kind of virus, worm, trojan, keylogger, spyware, or other malware. The only things any security scans ever complain about are tracking cookies, or occasionally "no CD" cracks back in the days when requiring the game disc to be in your CD-ROM drive was a popular anti-piracy measure. It's just not that hard to avoid being infected by malware, and I really don't understand how so many people get so completely destroyed by viruses.
