Can a daedric Prince create a portal anywhere he wants when he wants to? The portal won't allow daedra in but could a person walk in not knowing what it is? or do the barriers have to be weak in order for this to happen?

Whatever the rules are, the door to the Shivering Isles, and the portal at Boethia's shrine work after the gates to Mehrunes Dagon's plane are closed. Peryite's quest sends you back to Tamriel through a portal, and IIRC the shrine is acting as one in the other direction. Certainly travel between the planes has not been stopped altogether.

Maybe only Mehrunes Dagon has this power taken away?

I've always imagined them as more of stargates than interdimensional rifts. As for whether or not they can be opened, it seems that there isn't as much of a restriction as long as the portal is either one-way to Oblivion or only useable by mortals.