Tuning guitar from std to e flat, change to a new string size?

The "maintaining tension so the neck won't warp" thing is BS. Nothing to worry about there. So just tune down and see how it feels.
 
In terms of tension, there are guides and calculators out there where you can look up tension of a given gauge tuned to various pitches. But if he changes strings with any frequency he can just experiment and see what he likes.

I used to tune E flat, for 20 years probably.  Always used 10's.  String bending was a little easier, I guess, but enough difference in a half step to really matter to me.  

I have a coworker who bought a guitar for his 6 yo son, so I looked a couple weeks ago for a video on how to set that up. It is pretty nicely done, and part of the steps apply to setting up any guitar (that part starts at 3:10, and the video is more about grabbing "any" guitar and making it playable):
 
For what you are doing, steps 4, 3, 6, 7, and 8 would apply (what tlw mentioned above).

1. Clean it up
2. Tighten it up
3. Adjust neck (truss rod) - so very little height in middle when fretted at both ends... do with string gauge to be used (if change string gauge, do 4, then 3).
4. Change strings - 0000 steel wool to polish fretboard and frets, linseed oil fretboard, graphite (pencil) the nut saddles
5. Pokey frets? - tape off and sand with nail file (emery board)
6. Saddle height adjustment - any buzzing after setting truss rod
7. Pickup height - lower on bass strings and lower on neck pickup
8. Intonation - FFF = Fretted, Flat, Forward - Is the fretted 12th fret flat (when open is in tune)? Move saddle Forward (toward the nut). 

Skip ahead to 3:10 (the beginning is about finding/buying a guitar)
https://www.youtube.com/watch?v=12qmuB3yo7Y

mettelus

Adjust neck (truss rod) - so very little height in middle when fretted at both ends... do with string gauge to be used (if change string gauge, do 4, then 3).

0.012 inches (12 thousandths of an inch) is a typical amount of reliefe needed - measure by putting a capo on the 1st fret (or otherwise pressing the strings down there) and fret the lowest pitch string where the neck meets the body, Then measure the relief between the top of the 7th and 9th frets and the bottom of the strring. Tighten the truss rod to decrease relief, loosen it to increase relief. Go at most an eighth or a quarter turn of the rod at a time with the strings slackened then retune and check again. It usually doesn’t need much of an adjustment to sort things out. Slacken the strings before turning the rod then retune before taking a measurement.

The idea is that the strings have room to vibrate all the way up and down the neck, the lower the action the greater the relief that’s often needed. The gap isn’t critical so long as the guitar feels good to play and there’s no fret buzzing going on.

mettelus

Change strings - 0000 steel wool to polish fretboard and frets, linseed oil fretboard, graphite (pencil) the nut saddles

Linseed can be a bit sticky. Lemon oil is usually a better choice for fingerboards, available from any good guitar shop. Wipe a lttle all over the board then let it soak in for 30 seconds to a minute and wipe off. If it disappears into the wood in less time than that apply a very little more. Do not oil a maple fingerboard, only rosewood/ebony and then only if it’s not lacquered. A dose of oil twice a year, spring and autumn, is usually enough. The idea being to help the board cope with the temperature and humidity changes. Try and keep the oil off the lacquer.

mettelus

Saddle height adjustment - any buzzing after setting truss rod

I generally set the action and intonation before looking at the neck relief - if the action’s too low then the relief will either be huge or not even possible to set before the rod goes slack. If the action’s too high then it’s too easy to set the neck with an upward bow in the middle which will cause all kinds of problems.

The action, intonation and relief can all interact with each other, so going through the process a few times is often needed, getting closer to the desired setup each time round. If the process seems time consuming and tricky on a guitar, then try setting up a banjo. :-| Or a Fender where the truss rod adjustment is at the body end of the neck so setting the relief can mean dismantling the neck out of the guitar.