It has always been standard when riding to pass on the left; left shoulder to left shoulder. Same as vehicles on roads, so this should not be an issue for anyone, but just in case, I always call out "passing on left" esp on multi-use trails when I meet a biker. So far have never seen runners on the mountain trails we ride, but it could happen I guess.
As far as muddy trails go, I don't try to ride on muddy trails on purpose, because it could be dangerous on the mountain trails, however, we have run into muddy spots, and sometimes they can't be avoided.
The trails I ride on used to be horse only, then at some point the bikers wanted to ride them, so they became multi-use. Now the water crosssings are all gone, covered with bridges and culverts, and stone keeps showing up on more and more of the trails.
This is not a benefit for the horses, and honestly, I don't understand why the trails changed to multi-use. There are plently of walking trails that could have been opened up to bikers, and a whole other mountain range with bike trails, so it is a bit hard to see the horse trails, when those are the only ones, be taken over by bikers.
Not to mention all the forest roads that the bikers can use.
Nothing personal against bikers, but horses never seem to be allowed on bike trails, so why do they have to be on the few we have?
Just my two cents.
I will try to answer your questions as best I can. FWIW, the majority of our trails are multi-use, but we have a unwritten agreement that certain ones are horse centric, usually sandy trails or trails with not much "flow" so these are nice for horses and not so much for bikes.
Bike centric trails tend to have more slickrock around here and are close to cliff edges or mesa edges.
We do have a couple bikes only and horses only trails systems and that's nice.
The Back Country horsemen here in SW Utah have built less than five miles of trail (and that's being VERY generous) in the last ten years while the mountain biking community has built (and PAID for) well over 100 in just the last five. Also, when trail maintenance days take place, they are nearly void of equestrian rider volunteers. Don't know why that is..just that it is.
If I were you, I would reach out to the mountain biker community and not just tell them what you prefer to see, but rather show up with a bunch of equestrian volunteers on trail maintenance days and help. We don't have much in the way of water crossings here in SW Utah, but up in Sun Valley, ID where we go in July and August, the stream crossings are preserved and bridges built as alternate routes for those not wishing to get wet or use during high water times. I like that a lot.