Seemingly simple question.
The idea is that I want to go and return in one day to Hiroshima. That with the trains using the JR rail pass. From Tokyo.
Get on the train 8:30 in the morning, arrive in Hiroshima 13:30 .. go around sightseeing for 3.5 hours and get the train back to tokyo.
Can I do that?
Is there any limitations? Or JR rail pass can be used 24/7?
Thanks in advance.

Sure.
There are some bullet trains you cant use.. can't remember which ones.. but you can use others, so no problem.
Ask these guys: http://www.englishfriendlyjapan.com/japan-rail-pass

As per the forum rules, I cannot place a link. But I can suggest you do a Google search for Hyperdia which is a timetable of trains on the JR line.

The Nozomi and Mizuho Shinkansen are the two that you cannot use with a JR Pass. All the other Shinkansen lines are accessible.

I don't know if either the Nozomi or Mizuho lines go directly to Hiroshima without requiring a transfer. But my experience going to Hiroshima on the Shinkansen with a JR pass involved a transfer at the Shin-Osaka station.

You're running a very tight schedule and if you're doing any sightseeing in Hiroshima, the Peace Museum is worth taking the time. There's also Miyajima which isn't too far away and if you have an interest in visiting that shrine, you will need far more than the 3.5 hours you mentioned.

The pass cannot be used 24/7 because the trains simply don't run 24/7. The only restrictions I'm aware of are that you can only use lines owned by JR. Therefore, municipal subway systems and private railroads are paid for separately. And the restrictions I just mentioned about the Shinkansen. Otherwise, you can use that pass as much as you want...during their opening hours of course.

I hope this helps.

Cheers!

Jon