when you click on a topic during a quest.

What would cause some of a mod's quests to work and others to make your game crash?

it get's weirder when these are the prerequisites:

1 - I installed the game properly.
2 - I installed the mod properly.
3 - The mod list-requirements are in order.
4 - All vanilla quests work.
5 - Half of the mod-quests work.
6 - This issue has not been present for anyone else who tested the mod.
7 - The game crashes when I speak with a quest-character about the topic of my current quests.

I am really needing to test this mod out, because of a promise, however, this is preventing me to do so, and what makes things more difficult as I have to leave on Monday, and won't be able to return for a long unknown amount of time.

It probably has some scripting stuff attached to that topic. Open up the mod, find the topic and who said it, see if there's anything in the result box.

But, if it was a scripting issue, wouldn't this same problem be experienced by other testers, which I must say, has not been, and others have played the mod quests that don't work for me, fine and without issue.

Aye, but there could be a variety of other factors in a script, which is why you should check the results.

As my scripting understanding is basically zero-to-none, in dialogue, is variables/functions a script to a dialogue?

Try to play it while you only have the other required mods running. Maybe it's a conflict or something (you never know)
Have you updated your exe? MCP, Timeslips Exe Patcher, 4GB Patch

Anyhow, if you're testing it and you can't go any further than that quest due to crashing, you'll just have to report that bug to the modder.

The required mods are running. And this hasn't happened before when others have tested these very same quests. Currently, someone is testing the dialogue to see if there is something wrong, but somehow I doubt there will be. It has to be something that is unique to me.