It was not to have problems ...
On the second problem, the character cannot run. No, is set to "Underground" instead of "Inside". See:
Why this is happening?
EDIT: The second problem I fix changing set the "Show name on entering" to "??? ". But the first problem persists.
This might be a complete hunch, but it might be that your offset is an odd number. The game seems finnicky about odd numbers as an offset...if you look in the original games, I don't think any map has an odd number as an offset. I've had a few in my game that cause problems, and a few that don't. I can't think of anything else, though :\