I purchased these two trees at the same place I took my beginners Bonsai class. I have all I need to re pot but have read conflicting articles on when to re pot. I don't want to stress them out and I don't have any place to plant them. The instructor told me I could re pot them, but I read other wise about azalea and maples. The training pots have holes and I just fed the maple today. Any opinions and advice will be taken under serious consideration.
Questions are also welcomed.

I have tried numerous ways to turns photo's on an iPad and would love to have someone enlighten me.

First, you only need to re pot if it is needed. Also Azaleas and Maples are usually re potted at different times, Azaleas after flowering and Maples in spring before bud burst. I hope you only took them inside to take pictures.
As long as they are draining well there should be no need to re pot. You should have asked when they were last re potted also, as it is normally every two years for young plants, and longer for older mature trees. You should not have added any fertiliser as the Maple is not in leaf and it is a bit early for the Azalea. Depending on what country you are in and when your spring arrives you should wait until bud break before adding fertiliser.

Thanks.. I didn't fertilize the Azalea. The Maple only got a small taste of diluted liquid plant food.
The pictures were taken on my patio (outside). These tress won't see inside at all. I have a small green house for freezing temperatures.
I will find out about the last time they were potted in their existing pots. I read that Maples are susceptible to root rot, so I was curious as to potting it in Bonsai substrate. I'm in the north eastern part of the USA. My spring is just about to spring
Thanks again

That's fine. The azalea does need a bit of protection if it gets very cold, below about -6C and if it is wet a lot in winter. Otherwise it if hardy. The Maple should be fine outside all year. The Maple will only suffer root rot if it is vey wet for a long period of ti,e.

any advice on when to wire would be appreciated also.

Spring is a great time to wire, but you need to pay attention to the growth.
For the maple: Those young shoots will thicken quickly, and the wires will start to bite into the bark if left too long. That will leave a twisting scar. Once you see it happening, use wire cutters to nip the sections. Don't try to unwind the wire; you risk damaging the bark even more, with bigger scars, and bigger chance of losing the branch. If the branch springs back in place, you can always wire again. Repeat.
www.bonsaiempire.com/tree-species/maple

For the azalea: use the same method as above, but be careful of severe bends. Azalea isn't as forgiving as maple.
www.bonsaiempire.com/blog/azalea-shaping

I think I'm going to leave both trees in their pots until my wife and I purchase a house. Then I can get them reestablished to a new environment. I wonder... can train them in their existing pots?
I would think so.
I've read on here that the trees health is paramount. So I don't want to stress them out.