This game is seriously just bugged to the point where I can't even play it. Almost every single quest I've gotten is bugged so far. People not where they say they'll be. Bugs where when I pay for a room in an inn, and rest, I get arrested. Bugs where I rest in a guild hall that I'm a member of, I get arrested, when every source says I should be able to do so. Bugs that give me quest that are for level 30-ish players when I am level 2, and when I decline, I get kicked out of my guild. Lol? Fun times. Bugs where I cannot loot piles of loot no matter what angle I am at, no matter if I'm even crouching right on top of it. Bugs where I get arrested for going into shops when it's 2 PM. "HALT!"

I mean, like, what? I just don't even understand this. I'm trying really really hard people. I really am. I'm trying to get into this game. But I simply cannot play it because every single corner I turn, I am running into a bug.

Is there some sort of a patch or an unofficial patch I can download to fix this broken game?

Use the Daggerfall Setup from UESP to get a fully-patched version of the game is all I can suggest.

I dl'd the game through the official link on this site. Shouldn't that suffice?

If you followed the instructions for installing the patch it should be pretty playable, try the http://www.uesp.net/wiki/Daggerfall:Files for more help

Regarding being hassled by the guards, what is your legal status? They want to arrest you for criminal conspiracy if your status in the province is pond scum or lower. And of course, Daggerfall guards will find you anywhere. I'm surprised they don't haul me out of dungeons.

The following is my tl;dr advice from a Daggerfall new player who has done a fair bit of research:

As for the rest, yeah, welcome to Daggerfall. I'm not sure I get it either, but I'm getting some fun out of it (been playing for a couple of months or so). I find gaming the system and RPing around the bugs is a neccessity. If I hear you correctly, the real frustration comes when the game doesn't play by its own rules. But when you begin to understand how the game breaks or glitches it's own rules, you can kind of follow those rules and get back to the game. Not sure if that makes sense-I haven't finished my coffee

Also, if you can adapt your gaming style to the game it helps. Don't be afraid to fail: go to jail, get your butt handed to you, get kicked out of a guild (only really svcks for the Thieves and the Brotherhood), or run away from everything for a few levels. Everything short of death is part of the game. If you are RPing, this can add to your character's experience.
If your copy came with the original manual it can really help you understand the developers' sense of how to best experience the game.

Lastly, I haven't checked your link, but there is a link on the UESP wiki to a DOSbox/DF fully-loaded and patched bundle. I use this; however, it's still bugged. Many features simply don't work as described in multiple sources and versions. Also, the host site is French language, so I still come here or the UESP to gripe.

Remember, this is before the creation kit so the wonderful community of modders and fans has had more limited tools to fix DF.

Yes, there's a lot of quirks. For example, a Knightly order may kick you out because your reputation with the state is too low, even though your rep with "Generic Knightly Order" is high. Some of their quests may improve your state-wide situation, but most won't.
There's one quest that drops your reputation with an entire province, just because you got it. If you joined anything there, you've got problems. And the reputation system isn't visible without save editors, except for a few crude generalities (whether you're revered or pond scum in the current province).
Just go somewhere else for a while to escape the persecution.

I went ahead and searched online for an unofficial patch and added that. Just like the unofficial patches for Morrowind and Oblivion existing to continue to patch things after Bethesda stopped.

Supposively it fixes a lot of these quest bugs.