Regarding the sound stutter problem, I don't have it, and I can't help, sorry. I remember having read something about the weapon swing issue in Daggerfall Unity, but not in native Daggerfall. You may search the internet for something like "daggerfall weapon swing". Or someone else can help.

It would be useful to know your PC configuration, and if you are playing Daggerfall (GOG version) without modifying the configuration (of DOSBox, for example). You may also try to install DaggerfallSetup and test weapon swinging there (shouldn't make a difference, but it's always better to make sure).
And please describe how you move your mouse across the pad. The weapon doesn't react when you move the mouse a little bit only (there may be a way to change mouse sensitivity, but not in Daggerfall, to my knowledge). It may also happen that the weapon doesn't react when you move the mouse briefly and then stop. Drag your mouse across the pad continuously from right to left (or up and down) and back a couple of times - does your weapon still not swing? With some practise, the swinging system works well.

You may or may not like weapon swinging in Daggerfall, but this is the way it was designed and implemented by the developers, and it's not an issue of the GOG version. You could install Daggerfall Unity and link it with the GOG version (or with DaggerfallSetup). There you can enable the "click to fight" setting, which lets you attack by a mouse-click. Perhaps this is more to your liking.

To rephrase a point Greywolf1 made: the GOG version's not a port. All three widely available versions are literally original, official game files supplied by Bethesda & running through DOSBox; no additional work was done for any of them...and, apparently, even less work was done for the recent Steam release (though I guess people could've been wrong about that).

To fix the audio (and video) stuttering, try increasing or decreasing DOSBox's emulated CPU cycles with Ctrl+F11 & Ctrl+F12. Once you find a setting that works on your particular computer, you can edit the DOSBox config file for your Daggerfall installation so that it'll start at that CPU speed setting automatically on subsequent launches. (And just to head off a common complaint: no, GOG couldn't have set the cycles setting to "the right value" in the first place, since emulated CPU speed is still going to be affected by the speed of the actual hardware that DOSBox is running on -- so DOSBoxed Daggerfall (or anything else) will probably perform differently on a run-of-the-mill 10-year-old laptop than on a brand new gaming PC using the same DOSBox config.)

No idea about the problem with swinging your weapons. (You are clicking and dragging with the mouse button held down, right?)

If you've never really played Daggerfall before, I would second Greywolf's suggestion to use Daggerfall Unity (which is a fan reimplementation in a new engine, which helps modernize the game and cuts down on the amount of jank).
https://forums.dfworkshop.net/viewtopic.php?f=5&t=2360

Apparently, there can be problems with using DU with the GOG version of Daggerfall.

Just noticed that Steam has patched Daggerfall to the latest version now. This means Steam Daggerfall, GOG Daggerfall and DaggerfallSetup are identical - version-wise at least (DaggerfallSetup has still more user-developed content).