I know I can try to turn things in the Empire's favor during the Greybeards council, but is it possible for me to support the Imperial Legion in other ways without doing the Civil War quest?

The reason for not doing the CW quest is because my current character is not a fighter but a businesswoman, yet she is from and lives in Solitude, is in favor of the Empire (but not the Thalmor) and has been good friends with Elisif the Fair since childhood and is her most trusted thane (so Ulfric killing her husband, another friend of hers, was a low blow). Like Elisif she considers the Stormcloak rebellion something that must be purged.

Are there some quests or things that one can do to accomplish this? I think I could perhaps just go as far as to "joining" the Imperial Legion without going further into the rest of the quest, but other than that perhaps there are other things one can do.

I'd say help out the East Empire Company, but that ends up helping Ulfric too. Completing the Cidhna mine quest in favor of the silverbloods stabalizes the city a bit.(And secures the silver mine which the empire uses to fund its efforts) Try to save the woman in the marketplace too so she can continue her operation.

Unfortunately I already went to Markarth and the woman in the marketplace was killed So killing Madanach ends up being favorable for the Empire? Hmm...I'll have to think a bit on how to accomplish this since I don't really think my character would go at it with a shiv against Madanach.

OTOH the Silverbloods are huge Stormcloak supporters so you could also roleplay that anything that hurts them hurts the rebel cause in the long run.

Is it even possible to prevent that woman from being killed? I thought it was scripted to be inevitable. I'd like to do it just to keep that questline from starting if at all possible. It might be my least favorite questline in the whole game and it's certainly one reason why I took such an extreme dislike to Markarth and never quite got over it.

Yeah you can prevent it, I did with a previous character, smacked the guy who was going to backstab her as soon as i entered the city. The quest still starts tho. I hate Markarth too but mostly due to how difficult it is to find your way around the city. It is a mess.

I like Markarth personally, it is confusing and kind of annoying at times but I just think it is an interesting city. That might also be a byproduct of loving Dwemer stuff though. As for supporting the empire, just ask around imperial territories and see if misc or side quests are given. I know the stewards to the throne also often have bounties you can collect on so again if you do those ones in imperial territory you would be assisting them. Last thing I can think of is just dungeon clearing of bandits and critters in their territory, making the roads safer and whatnot.

So many creepy, unpleasant and apparently unavoidable things happened to me the first couple times I ever went to Markarth... even though I got to like it a little better later on because of some of the nicer NPCs I met, it's just never lost that creepy cringe-inducing vibe for me.

I've never been able to prevent the killing, I think the one time I tried it happened anyway and I was right there in the middle of it and got waylaid into the convo that starts the quests. The last time I ended up with the note in my inventory and ignored it for a long time before I finally gave in.

I'm not sure but I think I may have avoided it this time so far... I saw the murder when I entered the city but I was working undercover for the Stormcloaks so I was able to RP myself a reason for completely avoiding the scene. I'd have to check my inventory to see if the damn note is there but IIRC I was able to walk around a different way and never got close enough to the scene to be pulled into the action. I think now it may just be a matter of not talking to any NPCs about the killing.

Of course I might go back there several weeks later to find the body and other witnesses still standing there, just waiting for me to come along. "Hey would you please come over here and get this quest going, this corpse is starting to stink up the marketplace and we can't move it until you ask us about it."

Not doing the Civil War quest either way furthers the goals of the Thalmor. The Graybeards' "wisdom" of absolvement on moral grounds in attempt to avoid ethical responsibility will not avail you.

Ok, but my character is not going into the battlefield in support of the Empire not due to avoiding responsibility or anything but due to her not being a soldier/fighter. Yet she is more than willing to support the Empire in other ways more suitable for someone like her.

The problem is, if the area destabalizes too much the forsworn will wipe out the city(Letting a legendary forsworn king rile up the remnants of the forsworn is definitely a bad thing for the region), and the Empire will lose one of it's main sources of funding and need to dedicate a number of troops to retaking it.