Aesthetic is near 100% of the value of a bonsai tree. A well done phoenix graft or Tanuki is valuable, and worthy of growing. "Purists be damned". Where tanuki get "dogged" is when they are poorly done. In my experience most bonsai clubs do allow, or even encourage the showing of tanuki, IF the fact that it is tanuki is admitted upfront. Where the controversy arises is when attempts are made to not disclose the origin of the tree. A well done tanuki is better than a poorly done "natural tree". I would not separate the juniper from the deadwood. I would continue to develop the tanuki.
Junipers, in general do not need to be repotted very often. They tend to be set back by repotting. If the media the juniper is in still drains freely I would not repot. Young junipers in training are only repotted once every 2 to 5 years. More mature junipers might only be repotted once a decade. Usually one must allow a full 12 to 24 months after repotting a juniper to all recovery, before doing any other serious training on the tree. So generally, if you repot, no pruning is done the same year. Wiring is not as stressful as pruning, so sometimes wiring is done the same year the tree is repotted. My advice to "go slow" with junipers is for those in northern climates, and those new to the hobby. If you have to ask, you are new enough that the advice to "go slow" applies. There are southern growers in for example Georgia or California, that can get away with being very aggressive with junipers, because junipers have a long growing season in southern states. As one moves north, the junipers have a shorter growing season and need to be handled with a little more care.
So if the soil for the juniper is free draining, there is no urgent need to repot. You can take your time, make contacts in your local bonsai society. I believe there are at least 2 societies on Long Island, and also a couple more in the greater NYC area. If the "local group" seems unhelpful, reach out to the other groups from the wider area. CLubs have personality, not all clubs are a good fit for everyone.
The second tree does indeed appear to be a gardenia. Gardenia jasminoides is the botanical name. THey are popular as bonsai. There seem to be a couple flower buds on your gardenia, they probably won't open for a couple months. Gardenia can be moderately winter hardy. Gardenia jasminoides is probably frost hardy to zone 7b. There are a couple more tropical species of gardenia, but for the "price" you probably got Gardenia jasminoides. G. jasminoides is probably the most popular for bonsai, and is used fairly often in Japan as bonsai.
Gardenia like an acidic soil. Since they are evergreen, I would not repot until middle of summer, after the new growth has slowed down and hardened off. If the soil the gardenia is in still drains freely, I would not worry about repotting this year. I use the same mix I use for my satsuki azalea for my gardenia. In general 100% kanuma is what I use, though in the past I have used a bark and pumice mix. Since I now keep kanuma around for the azalea, I've switched my gardenia to kanuma.
