Ok here we go...

First, you want to remove any mulch or soil touching the trunk of the tree. You really should see roots flaring from the base. Keeping moist soil or mulch agaist the trunk will harbor fungi and bacteria which can cause significant damage or death. The mulch should cover the rootball, stopping a couple of inches away from the trunk.

Your watering regiment seems fine for now assuming you are watering directly on the rootball, that you are decreasing watering when it does rain, and that you are in a primarily sunny area. Shady areas will need less frequent watering. To be sure that the tree is getting sufficient watering, you can check the soil a few inches down next to the rootball right before another watering. If the mulch is a bit dry, the soil beneath is lightly moist but NOT wet (if you can squeeze water out of it is too wet), then it is safe to water again. If the soil is dry several inches deep, you may need to increase watering but you should be very careful as overwatering is usually more dangerous than slight underwatering. If you have clay soil you will want to be more cautious about overwatering since a bowl can form and hold in water. This not only cuts off oxygen to the roots, but it also harbors soil born pathogens that thrive in wet spots. Remember that by september you should be backing off the watering quite a bit. During dormancy you should be watering none unless there appears to be draught. By next year the roots should be somewhat established and watering should only be needed about twice a week and eventually less unless the soil dries very easily.

David or someone farther north might help out with the overwintering issues.

Pruning dissectums is more of an art than a science IMO. You should prune it to the shape that you find most attractive, but I would suggest looking at some mature specimens of similar trees to give you some ideas on what you like. Generally you should prune major branches in late winter/early spring or in fall after the leaves have dropped to have the safest results. To be honest, I prune small limbs throughout the year and rarely have any trouble. However, it is a bit easier to see what needs to be pruned in winter because you can see the limb structure better. Also, I generally recommend pruning from the inside out (cleaning out the small twigs inside shows off the winding limb structure).

You can remove the stake if it will stand on its own strength and if you no longer wish to train it upwards. Garnet is a fairly upright grower, so it usually does not require much staking.