There is really no way of downgrading units, once they have been upgraded, right? AND! is there a way to divide larrger units into smaller ones, during battle?

Unfortunately, no and no.

Sadly this can only be done BEFORE battles or in between. However I cannot think of a single game where your allowed to divide stacks during battles so not sure why you would even ask.

Also not much reason to want to downgrade units thus no one ever thought to put that in. The only game where this might be useful is H5 because of the alternate upgrades, but even that is not really doable since you have to choose the building upgrade path prior and no way to change that later on.

the upgraded units are much more expensive. the price gap between the red and the black dragon is huge.

Actually the cost is only 500 gold more from Green to Red and 500+1 sulfur more to Black.

If you had the money to actually upgrade the dwelling this shouldn't be a problem. Not to mention that while their stats only get get a small boost, their HP goes up by +50 each time and initiative goes from Average>Fast>Very Fast which is quite important in H2.

Nevermind. I didn't notice the "during battle", nope, you cannot split armies in battle.

The cost of buying new copies of upgraded units is often not much more expensive than the base unit, however the cost to upgrade your existing base units in your army to the upgraded ones is hugely inflated.