Chris,
Thanks for the kind words. I have had some experience programming the old DX7, and I learned a lot from taking apart the factory sounds, as well as reading some out of Massey's Complete DX7 (but that was over 20 years ago, so I am dating myself). That was back in college, and we had three instruments: DX7IIFD, Oberheim Rack, and Roland MT32 (a poor man's D50). It was a good lesson in learning synthesis from the 3 popular synthesis technologies at the time, FM synthesis, Analog, and LA (linear arithmetic synthesis). Part of my philosophy of programming comes from the LA synthesis side - partials. I'll explain more in a minute.

To answer your questions:
1. On the brass example, some of the fine tuning I just played around with (not completely random, but to my preference). Try not to look to deeply into that part of the example. This is why: I used some fixed frequencies to enhance the metallic part of the tone. Fixed frequencies can be a difficult concept to wrap your head around, but they can be helpful for some specific parts of sounds besides sound effects.

2. On the ADSR - first think about generally what your sound is supposed to do (the amplitude part). Is it a sharp attack (low attack numbers) or is it a softer attack (strings, pad, etc.; higher attack numbers). This applies to the Carrier (bottom operator)
Then think about what the harmonics are doing, similar to a filter in analog synthesis. This applies to the modulator. (skip this if I am being too basic).
Sound is very dynamic, so sometimes you may actually have an envelope that decreases then increases again (I think I did this with the brass, but also with the strings).
How the Modulator and Carrier envelopes interact may also turn out a little different than you think. Sometimes, as with brass, you may have the Carrier attacking slightly faster than the Modulator (which gives you the initial "bwah" sound. With strings you may want the Carrier to come in slightly behind the attack of the Modulator. If you don't, even if the numbers are technically slow (40-50), it may have a hammer-like attack because both components are striking at the same time.

3. The coarse tunings are high to add to the metallic tone; yes, technically we are achieving more harmonics, but listen to it and see how it sounds as you are tweaking that

4. This is a lack of polish on my part if there is no change in the level, sorry. I think I was probably experimenting with something.

5. The spectrals I honestly had to play with. On the original DX7 we had just sine waves, so this is an enriching experience to be able to have more raw material to start with. The skirt I had to experiment with, usually starting with extremes of 1 or 7 for comparison.

Getting back to fixed frequencies: you can achieve a lot of sound emulation with the right parts, so don't be afraid to dive in with these. A lot of it sounds metallic, but sometimes that is the resonant part of a sound that you don't realize until you put it together.

When making a sound, I try to think of the parts of it. With LA synthesis, they said that the hardest part to emulate was the attack, so they included multiple kinds of sampled attacks. I sometimes use the fixed frequencies to emulate an attack because you can create the noise of lip buzzing, flute blowing, piano hammer, or bow strike with lower frequencies (around 10-100 Hz). You can use fixed frequencies for both Modulator and Carrier if you are only using that stack for an attack. Or if you are using the Carrier for the body of the sound, you may want to use a ratio with another Modulator (that is why I selected those particular algorithms).

For the body of the sound, I usually stick with the old standbys of many common analog wave emulations, e.g. M:C 1:1, Modulator level 85 for sawtooth, M:C 1:1 Modulator 78 for triangle, or M:C 2:1 Modulator level 81 for square wave, etc. (I don't remember if these are the exact numbers, I seem to remember these off the top of my head, but check with Massey or some other DX7 reference to be exact). Using detune on the modulator not only helps with chorusing, but also helps to keep the sound more organic.

For other types of instruments such as strings, I use some nonstandard ratios for some parts of the sound (e.g. 3:2) because it seems to emulate the resonance of the body of the instrument better.

Take a look at some of the popular old (and even factory) DX7 sounds. I am still amazed at what they were able to achieve with what seems like relatively simple parts now. I hope this helps!