Hi there.
I'm having trouble wrapping my head around the first issue involving the use of the escape key. When I was testing this a couple months ago, I noticed there were some issues when using multiple custom screens at once, e.g. MC's dorm computer AND the new event menu on a different layer. That should be fixed, and a quick test I just ran on my copy seems to back that up. Do you notice the same issue when right clicking with a mouse?
As for the relationship menu vs event menu, that's simply a compromise I made with the roll out of the new UI. The new event menu and original relationship menu don't get along, so I hid the event menu any time you're on the relationships tab. Bringing it back is as easy as navigating to any of the other tabs.
I'm not a ren'py expert, so if you or anyone else has an idea for how to get around that issue I'm all ears. Spent a solid couple weeks of trial and error, browsing forums, no dice.