The whole plant:

The single shoot of leaves is the normal output and the plant would decide to flower in its season. Sometimes two growth eyes will grow and then the orchid can be divided after a few more years.
"in its season" could be more or less straight away, in winter, or spring.....depends on which orchids are in the ancestry of your Slc. Hybrid.
In a similar vein, the size of your plant depends on ancestry.
Heading into Autumn, might not be a good time to fiddle. But you might be OK in AZ??????
Plant looks to be in reasonable condition and you want it to dry a bit between watering intervals, so be wary of media that does not dry a bit between those intervals. Sophronitis like to be a bit cooler and more moist than most Cattleya and Laelia. How much Sophronitis?
Only the name bit following Slc. will give us a clue.
Sorry, a bit of a ramble that doesn't answer your questions.

Your plant is nice looking but I fear too dark looking. You should have it in an east facing window where it will get morning sun or it can be kept outside hanging from a branch of a tree where it is partially shaded but only during the day when nights drop below 55 degrees F.

The media it was growing in was perfect for it and indicates the type of culture it was receiving. This commercial grower culture was probably watering this plant every other day with the room it was kept in with high humidity which I would suspect to be at least 65% relative humidity though up to 85% with fans running 24/7.
To your questions:
1: if you use coconut chips mix in at 1 to 1 pumice as little stones or gravel. Keep in mind that even though this is a hybrid this plant is genetically designed to live on branches which may be soaking wet during some time every day but is exposed to constant air movement.
2. I would recommend Miracle Gro. They have an orchid food that you can apply every 2 weeks when the plant is in active growth. When new growths have stopped growing stop the feeding. The link is below. Follow the instructions.
3. This plant should get some direct sunlight sometime during the day. Most likely early morning or very late afternoon BUT because your plant has been so shaded giving it any direct sun will probably burn it, especially the new growth. So see my comments above on the light. If using it in an east window just leave it in the window during early morning when sun hits it and remove after an hour and place in partial shade, outside if possible. Monitoring it when adapting to a change in light exposure is needed throughout the period of increased exposure.

While a lot of folk swear by hydroponics such is not suitable for this type of orchid unless the orchid is suspended above the water and not in direct contact with it except whenever you water it. So I would not soak the potted plant at all but rather water every other day.

Good luck.

Here is a link that might be useful: Miracle Gro Orchid food

Right now the new shoot is getting all of its energy from the older growths. The older growths will not grow anymore and it's normal for them to loose roots and eventually drop leaves. I don't think at this point fertilizer will do much for the plant since it is mostly using stored food now. In a few weeks the new growth will start growing it's own roots, that's when I would start to use fertilizer at 1/2 dose weekly.

Styrofoam peanuts are used a lot to improve drainage. Logees is on the East Coast which is cooler and more humid than Arizona. You may need to do some trial and error to figure out a potting medium and watering schedule that will work for your situation, it should retain some moisture, be coarse to allow air circulation and dry between waterings. It will need more light than the phal but be careful with bright light + high heat + dry air.

A plant that size can also be a few years from flowering. so don't get discouraged if it doesn't flower right away.

So I rambled a little bit, the real problem might be how to grow an orchid of any kind in Phoenix, Arizona.
Yesterday, here, might be more the norm for Spring there than here. Max 34C Humidity 19%. Shade-cloth set at about 80% to cope with the coming summer.

Maybe orchid growers in Arizona grow outside late Autumn, winter, early spring then have to bring everything inside to cope with searing summer temperature??

Well sphagnum moss takes forever to dry but that can be a problem too. I like the stuff from New Zealand and you can find it in pet stores too- kind of expensive. Some of the stuff that you get has sticks and leaves in it but not the stuff from New Zealand.

Hi Cooper, the NZ Spag. is excellent (and very expensive), but you have to adapt your watering intervals. Wonder where Cattleya heaven is in the USA?
They are mostly not cloud forest type orchids so you need a mix that dries fairly quickly.
It would help if the OP came back and gave us the name that followed Slc.

Yeah arthurm I've never tried it but I've heard Chilean Sphagnum moss is very plentiful. I'm going to try to find some.

Hi everyone,
Sorry that I did not get back to you all sooner.
First of all, thanks to everyone who took the time to reply.

Terrestrial man, I agree, it does need better light. It's possible that I can keep it out on my east facing porch, where it will get some morning sun, all the way until spring. But that all depends on how well the plant can tolerate the cold nights.

lumpy, the new growth already seems to have some new roots of its own on it, so I guess I should start to fertilize then?
I figured that that's what the packing peanuts were for, it was just strange for me to find those in there.
Arthurm, that sounds about right, High is 91F today, 17% humidity.
For the average person, growing orchids outdoors here year round is pretty much impossible because of the horrible summertime temps.
I do know that some people do grow them here year round, but they have special greenhouses with shutters on the ceiling that they can close during the middle of the day, and they need humidifying equipment too, which of course keeps the air moist but also helps keep the temp down as well.

Here's a photo of the tag. I hope it helps.

So what is a cold night? Down in the 40's F every so often probably will not worry this orchid which has some cool tolerant ancestors. One parent Slc. Jewel box is best grown in a shade-house rather than a glass-house. It flowers in spring.
Is there a local orchid society? They might have some tips re. the annual cycle of growing.
There are always some pluses and the plus there is all those sunny days.

Winter nights can sometimes dip into the 20s.

I might have to change my saying from "real orchid growers live in the frozen north" by adding "and AZ" to the sentence.
The lowest it ever gets here in the yard is about 1 or 2C.

Will shade-cloth help break a light frost and at what temps will damage occur to some Cattleyas?

In some sub-tropical places you get a cold night and the mostly sunny days warm the plants up.