Does time pass in the real would when you're in Apocrypha?

Yes and no. For human comprehension's sake, let's just say it's circumstantial.

Perhaps it is more accurate to say, time does not pass in Apocrypha. But "time" is still passing regardless, case-in-point, Miraak. It is likely the 3,000ish years trapped in Apocrypha felt no where near that long for him. But time certainly did pass, though he remained un-aged.

I think OP means does "in-game" time pass in Skyrim when you're in Apocrypha?

And from what I have seen in my game, yes it does.

Yes and no. I mean is the day passing normally in Tamriel when I'm in Apocrypha? For example, if I spend a day in Apocrypha would a day have passed in Tamriel?

I would just suggest using your own interpretation and personal preference. There is no definitive answer and a case can be made for both.

Personally, I think time does pass, but not on a 1:1 ratio. A day in Apocrypha would be like an hour in Tamriel or something.

I think time gets more wibbly-wobbly in Oblivion than Nirn, and is tied to the whims of the Prince whose realm you're in. Let's say Hircine only hunts for one hour each night in his Hunting Grounds. I doubt that hour is equal in length to all other hours in the Hunting Grounds. It probably is a year in length instead.

If you are asking how the game functions, then like I said above, Yes.
The game calendar time passes the same, regardless of where you are in the game. Time will pass for anything that was happening in Skyrim, but it shouldn't really affect any quests or anything.

He wasn't asking from a Lore perspective.
There is no personal preference for game mechanics... It either works one way or another.

I wouldn't say it's wibbly-wobbly, I think it's a bit more timey-wimey.

I would say that if Time in TES lore was ball shaped. However, we know it's actually shaped like a dragon.

I love Whovians.

I believe that each realm of Oblivion operates within it's own time, otherwise how do you explain Miraak and Yagrum Bagarn? It's possible the Prince who governs the realm is in complete control of everything including the passing of time.