As the topic says, somehow I am unable to kill dragons. They ressist everything I throw at them, neither others can harm them - with one exception - somehow I was able to damage one of them - common dragon, not the blood / frost / revered etc. type.... using conjured bow with the end result being death of the dragon - but it did took an incredible amount of time, longer than is normal. I ran the game using few mods when this bug occured, uninstalled all of them, uninstalled the game, performed the clean install, yet to no avail - bug is still present. I can, however, say that I am sure that this bug didn't happen in saves that were made 20 hours or so before the newer ones, where this bug occurs. I tried plenty of things and I am currently desperate, since I fear that even if I did start replaying the older saves, I could run into this particular issue again and, being unable to resolve it, my save games would become worthless. So my question is - do any of you know how to resolve this particular issue?

If you loaded the same save that had all those mods on it, then you would still have the conditions from the mod baked into the save that caused the problem in the first place. Basically, you can't remove a mod from a save, especially one that has any scripts on it, they get baked into the saves. This is why your current save still has the problem.

As you have surmised, you need to figure out which mod caused this, then remove that mod, or not install it again, then load up a save from before you started having the issue. Also, you need to fork a save when adding any new mods to a game, so you can remove a mod if it causes problems, then load up the save you made before you added the mod. This is the only way to remove a mod from the game, at least most of them.