Hello!
I have now played Archie's route, so I can offer more insight, but I haven't went back to Verdant yet.
It seems the issue happens when you are in the RPG inside the game as I haven't had the error otherwise.
Getting to the RPG screen is never an issue, but when something new happens once on that screen (most commonly this was when the MC had an inner dialogue on screen, so it needed to overlay on the RPG's chat interface, but it also happened when Astion's chat came through a couple times) it would freeze and there would be no dialogue on screen at all. The background would be visible, and the chat and dialogue box too, but they were blank. The only way I found around the issue was to save, go to the main menu, and load that save. When it has that issue, I can still interact with all the settings, but nothing else if that makes sense. I can get a screen shot, just give me a couple minutes to play through the route. :)
For skipping, I think that was user error, sincere apologies. I am used to renpy, where you can tab to skip. Using the skip feature in your side menu worked just fine.
Also, please note that though I mentioned Verdant's route, this issue also happened on Archie's, just much less frequently.