When playing Syndicate Plus, during missions, my mouse flashes and sometimes 'glitches out' like freezes on the screen momentarily.

Might be able to live with it, but would be very nice if there was a fix.

Installed the game as Admin, running as Admin; tried running in compatibility mode for Win 95, as well as with
disabled visual themes, desktop composition, and DPI Scaling.

Anything else I could try?

Also sort of a side question, but what do the options when booting up the game for the first time exactly do?
I left them at default.

All that Windows compatibility stuff doesn't really help much with Dosbox emulation, try selecting a different video output in Dosbox.
As for starting the game for the 1st time, those are soundcard settings and are best left at default.