Do you think its possible to have the camera shaking when in sprinting mode also appear when I run or walk? If so, how?

Reason is that I always feel like a floating camera because there is no real movement feeling when ... moving.

Or is there a mod that adds this (not the buggy first person mod where you can see your body).

You dont even know what you are asking for buddy, thee is a mod that does this for Morrowind and it is absolutly nightmarish after awhle, it looks cool when sneaking arround but for prolongued gameplay it is really annoying

There's a "See Your Feet" mod, or something similar to that name that puts all (most?) third-person perspective animations with a first-person view. I'm not sure how much has progressed with it as it did have some bugs, but it seemed to be working for the most part. That mod has the shake you're looking for even when you're just walking.

I saw one of the review-type videos on YouTube review a mod that did this, at least in first person, but it moved the camera around for combat too, when you swung a weapon. He said it was a little over the top. I like the concept, but the modder would have to be careful not to overdo it.