You have a lot of things right, a few things need adjusting.
Yes, the shafts project a bit too far forward; their tips should be about even with the point of the horse's shoulder--as Al said, try lengthening the traces by one slot. When you do, you will find that you need to readjust the breeching holdback straps.
Yes, the shafts are a bit low; raise the tugs(tug loops) by one hole (when you do, you will find you need to readjust the wrap straps!) Shafts should be level to inclined SLIGHTLY upward, back to front; there is no 'hard and fast' rule about them 'lining up' with the traces; in fact, this happens only in carts like the EE(easy entry) pictured, where the singletree is mounted about level with the shafts. Better is a lower 'line of draft' (draught),but such is seldom found in 'pipe' carts, such as the Frontiers and other EE carts.
The breastcollar is a bit LOW; try raising it by a hole, maybe two. It should rest JUST where the neck 'joins' the chest, and should NOT rest directly 'on' the point of the shoulder.
DON'T put the breastcollar neck strap over the waterhook on the harness saddle, and DON'T do without the breeching! Such things are ONLY for the roundy-round on firm, level ground of the breed show ring, where you will find many if not most, horses actually pulling the cart off the harness saddle, via the tugs(tug loops), and not the breastcollar, via the traces, as they SHOULD. EVERY horse should be trained to accept and understand breeching; it can be 'removed' for (breed) showing, but is a GREAT benefit to the horse pulling a typical two-wheeled cart in the 'real world' of driving. It is essentially your BRAKES! (You WILL see harness w/o breeching in the ADS pleasure world, but ONLY with 4 wheeled vehicles with BRAKES- which are balanced, and pull, quite DIFFERENTLY than two wheeled carts, with only the RAREST exceptions.)
The open bridle is fine, at least to start with. There ARE good reasons for using blinders, however. Blinders are required in the show ring, too--so it is best for the horse to accept them, if possible.
A caveson's actual 'legitimate' purpose is to keep the cheekpieces of the bridle from flexing outward, possibly allowing a horse to 'peek' behind its blinders, which *might* be a safety issue, so it might be best to use one, but adjusted high, as Al mentioned and reasonably snug(not TIGHT; its purpose is NOT to 'prevent' the horse from being able to open its mouth, as some think!)
A moderately adjusted side check is a perfectly legitimate way to aid in preventing a horse from trying to reach down to 'grab a bite'; once you are further along in training, it should be largely unneccessary.
It looks like your harness has 'wrap straps'; just be sure that they are not adjusted so that they are so tight that they exert downward pressure on the shafts, but do keep the shafts from 'flying' upward as you mount/dismount the cart. Once the driver is seated in the cart, you should be able to see that there is only a little 'weight' on the shafts as they rest in the tug loops. Ideal is for the shafts to lightly 'float' in the tug loops, but that is harder to tell about w/ wrap straps. In my experience, many people 'overtighten' the wrap straps.
Overall, looks as if you are off to a good start! Congratulations....
Margo
Driving and training to drive since 1985, and still gaining additional knowledge almost daily.....