I will attempt to answer your question to the best of my knowledge, but keep in mind that I don't have access to any information that you don't also have access to, so technically these responses aren't anything more than educated guesses. That being said, here are my thoughts:
Can a Ruler or Chief Warlord order all of those things to be done? The short answer is "Yes." The long answer is "Yes, but it probably won't do any good and would be a much better idea to not make those orders at all."
1) Casters changing specialties.
My guess is that it is possible to order a caster to cast spells from a different disciple as if they were a caster from that discipline, but I don't think their discipline would actually change. It would be like ordering a piker to shoot arrows. It can be done, but the piker is still a piker and not an archer. It would probably be in a leader's best interest to refrain from doing this in most instances, since your units are probably much more effective when they do what they are naturally good at. We know Wanda can cast Hat Magic, but we also know her resulting Snow Golem was an abominable wimp. She can cast a spell to control Jillian, but she isn't good at protecting herself from the backlash when the spell breaks.
2) Ordering attributes to change.
You can order promotions and demotions (such as Chief Warlord status) which may grant or take away abilities, but I don't think you can flat out trade attributes without some sort of magical help (probably Weirdomancy). If you order a twoll to fly, it might jump out a window, but I doubt it would defy gravity.
3) Ordering a unit to level.
I don't think a unit would go up a level from the order itself, but may make an attempt to accumulate the experience necessary to level.
4)Would such orders test a unit's loyalty? Or risk disbandment?
I think these types of orders would often test a unit's loyalty. Simply because when someone orders you to do something impossible or unwise, it would make you question wether or not this is someone who really knows what they are doing and are worth risking your neck for. As far as disbandment goes, I think attempting to fulfill the orders you are given is good enough. If something can't be done, it can't be done. But if it can be done and a unit doesn't do it anyway, then they better start worrying. The intent seems more important that the attempt, which is why orders can be disobeyed without causing disbandment when the unit is convinced it is in their ruler's best interest for their orders to be disobeyed.
When you frame it like that, I guess it isn't as much the Parson-Ex-Machina I had expected it to be. So you can order a unit to do whatever you please, but issuing an order will not alter Erf's physics to fulfill the order. That's up to the unit.
Makes sense, in a very logical way.1.)
I had never really considered that casters have huge fundamental differences, like a piker compared to an archer. I just sort of figured that magic was magic, and the casting ability was mostly preference. But you're right, and you couldn't have picked a better metaphor.2.)
Commander - "Stop being a heavy and fly!"
Twoll - "Yes lud"
Commander - "Go Level!"
Subordinate - "Okay"
Subordinate has stabbed the Commander. Subordinate croaked the Commander! Subordinate gained a level!4.)
Now that I think about it, that's exactly what Benjamin did in Transylvito. How did I forget about that?
The whole Weirdomancer thing gives me a different idea, though. If you linked a Thinkamancer with a Weirdomancer and some other caster, the Weirdomancer could feasibly assign the other caster a new magical forte. Even one on the number axis of Naughtymancy...
My goal is to create a Retconjurer that can delete equipment and specials, or at best single units (Only titans have enough power to retcon past events on a grand scale). Alternatively, a relatively weak side with this option and three casters could use one as 'tofu', taking on the necessary flavor for each situational 'dish'.
Either way, I guess I'll be doing more reading about Weirdomancy. Look's like it's back to Parson's Klog for me.