So I want to play Daggerfall on my DOSBox, but I'm experiencing the following problems.

On Fullscreen mode, when I try to skip the opening sequences, the game blacks out until I get the DOSBox out of fullscreen mode.

The game generally runs smooth, but with with occasional pauses in sound and motion, like a flickering lag effect where it's possible to play, but it's just annoying.

What solutions, if any, are there to fixing these?

I've experienced these same problems.

I've found that if you use the left mouse button instead, the screen won't black out (at least not as often).

Running a game in DOSBox is nowhere near as efficient as running the game on real hardware. On top of the standard performance hits you'll get from emulating a DOS machine, DOSBox itself is not a very well optimized emulator.

You could try running the game in a Virtual Machine (ie Virtual Box) but then you'll need a real copy of DOS (or a copy of FreeDOS, if you're even more technically inclined). Alternatively, if you've got a Linux box lying around you could throw dosemu on it and use that, as it's the most stable and best performing DOS emulator available.

Nevermind, I just had to change my laptop's power plan. Boy, do I feel stupid now.

Ah yes, one other thing: on Windows if you Ctrl+Alt+Del and open the Task Manager, move to the Processes tab, and Right Click on DOSBox.exe, you can set the priority of the task to "High" which should reduce the occasional stutter you feel when a background process wakes up or something.

With the dosbox setting under,

[sdl]
priority=higher,normal

you can set it to have a higher priority as it starts up and lowers when you move to a different window.

I've got it to run fairly well on dosbox, but the text that appears when you reach a destination disappears too fast.