Hi Carrot,
I agree with Rockm regarding the soil and repotting into a free draining mix, as this will safeguard against root problems further down the road.
To be perfectly honest though, I think the tree is in pretty good health if the photo's are recent. The yellowing leaves could well be last years foliage that didn't drop in the winter that is being replaced now.
All of my elms are currently doing this and have been for a couple of months. I wouldn't worry about the reddish new growth either. Mine have/had this too and continued growing and soon "greened off".
The best thing is to quit fussing over the tree so much. I know that sounds wrong and if I was saying this to your face you'd probably look at me as if I was from Mars or something lol but, 90% of the time its the worrying and "helping" that kills a tree. Its how I killed my first tree - a Chinese elm
. Being observant is good, inspecting your trees daily for bugs, abnormalities and soil moisture is a very worthwhile and recommended practise to get into, but playing with them isn't.
Its a phaze everybody goes through when first starting out, largely because of the myths and misconceptions surrounding bonsai, but once you learn about your tree, its growth habit and how to care for it properly, those myths about bonsai are dispelled and you'll think to yourself "what the hell was I worried about?".
Please don't let this discourage you from posting questions, as everyone here is more than willing to help and answer any queries you have. My intention here is to attempt to put your mind at rest somewhat... and I've probably failed miserably
.
All the best,
Aaron