On my current game save, I have quite a few problems:

1) The Dremora at Dagon's Shrine don't respawn.
2) Ore veins don't respawn.
3) I can't interact with the weapon racks in any of my houses.
4) Giants don't respawn anymore.

And yes, I've spent hours looking up all the bugs/causes/solutions/respawn times, etc. and I am at a stand still.

Will I be forced to create a new character if the next patch doesn't address these issues?

Many patch fixes are NOT retroactive.

You may need to restart, we will have to see when they come out though, those bugs sound fixable via retroactive fixes.

All I know is if my saves stop working time to get the dark brotherhood.

Bethesda are not GSC. So no, they will always be compartible.

I hate the fact that most bug fixes are not retroactive... That said, I think you will need to start over if these are fixed

So if I create a new character right now, I risk that save being effected by these bugs?

Such a shame.

This is why i tend to make a lot of throw away characters aside from trying out different play styles and such before I commit to one for the long haul it also buys me time to wait for patches to clean up a lot of bugs.

Well honestly, if this is the case I'm almost feeling burned out on the game. I want to create a new character and focus on Conjuration/Light Armor/Two-Handed, but seeing as that would almost be a waste I'm considering waiting until all these bugs have been patched.

Not exactly, but say you want to put armor on your mannequins, but they haven't fixed the bug with them turning transparent (which they haven't). If you interact with it, causing it to bug, then that bug will stay in the code of the mannequin, thus it would be unfixable without a bit more work on Beth's part. Just like the broken bookshelves bug. If you use it while it is capable of producing a bug, then it will stay bugged after the patch. Simply recreating a character doesn't do it.

So, if I create a new character and completely avoid all of the problems I've been having (ie. weapon racks, Dremora), the bugs will not be 'produced' so to speak in that current save?

That is correct.

EDIT: correct regarding weapon racks, bookshelves, mannequins (when they are fixed).

How you will avoid Giants is tough to say, as they are everywhere. Dremora should be easy, just avoid quests where they appear and you should be fine.

Ore veins take a long time to respawn, so that may not even be a bug. You have to be out of the cell of ore veins and ingredients for 30 days or say for them to replenish.

My first few character were throwaways, and I basically ran them with the attitude "Don't get too attached. Just run 'em through and let's just see how broken this game is." (It's not my first Bethesda game).

WIth my latest character, I'm treading water, so to speak. By that, I mean I'm staying away from quests that I know are bugged, and I'm staying away from player-owned houses altogether. The first thing I did after getting out of Helgen was get my character hitched and then I moved into my spouse's home.
For now, I'm just doing random explorating, dungeon-diving, collecting bounties, and doing some miscelleneous questing. Won't be doing anything significant until I see where the next patch leaves us.

A save contains all the information on explored cells/entities/NPCs/scripts and variables. If the bug is related to a bugged item (ie a container, a quest item, a quest already taken) it will remain bugged even after the patch will fix the master file.

Technically, it could be possible to patch the executable so that each time it loads a game saved with an old version of Skyrim it looks for known bugs affecting certain cells, NPCs, items and fixes them. The real question is: will Bethesda care enough to do this?

Most bugs like failure to remove bard quest items upon completion will be fixed game-wise but not save-wise, hope that makes sense.

You can fix those via command console.

Bugs related to spawns or anything that gets regenerated or recreated will be patched, eventually.

Objects who are bugged will usually be fixed in an patch. However the patch might fix the base object of an mannequin and not the one you have in your house.
Same goes for quests, an patch might help if you are stuck or it might not depending on the nature of the bug.

Starting an new game will always fix it, savegames is actually an mod who is loaded last and this might overrule patch information.