Can matter, energy, or information travel from one universe to another in a Level I Multiverse? That is, is there any communication between Hubble volumes in an eternal inflation-induced multiverse?
The answer is no by definition, since level 1 universes are separated by a cosmological horizon. If they weren't separated by a horizon they wouldn't be seperate level 1 universes.
It's a general feature of separate universes that they are causally disconnected. It's the fact of causal disconnection that makes us treat them as separate.