A couple of things I have just recently noticed

I'm sorry if this is old news, but I just noticed a couple of odd things that happen in the game.

First, after taking a capital city, one normally first repairs the city's structures and then hits the retrain button to bring the various units that have lost troops back up to full strength. One will see the costs for these activities deducted from their treasury just like they do when first building a structure or hiring new units. However the game makes one wait an extra turn for the troop replenishment while the structures are being rebuilt.

Occasionally, when I was paying attention, I seemed to notice some troops took longer than two turns be replenished. What I finally discovered is that unlike anything else in the game that takes more than one turn to be built or trained the money you spend on unit replenishment is not reserved until the troops are retrained.

What this means is that after you specify troops to be retrained, and your are in the situation outlined above, which makes this process take an extra turn, I think that the funds get added back to your treasury on the next turn. You can check this on the next turn by taking the retrain option off of a unit. You will see no funds added back to your treasury, but you will see funds deducted again if you reverse the process. Consequently, if you happen to deplete your treasury to an amount that is less than what is needed to train all the troops you have specified, they will not be retrained, and they will continue to not be retrained until the balance left in your treasury is sufficient at the end of the turn. ( I say that the funds are added back, but I cannot be certain of this since a lot of factors effect ups and downs of your treasury each turn. If they are not being added back then this is a problem that needs to be addressed.)

In early game when you are most likely emptying your treasury each turn just to survive, you need to be aware of this if you are in more desperate need of getting your units back up to strength.

Secondly, I recently captured a city that was fortified, so I had a star fort to contend with. I usually just stand off at a distance and bombard the interior with my mortars until the enemy sallies, which is always unorganized and easy to defeat. I also usually just blow a wall down and march in when the fort is empty. The advisor always warned that buildings I damage on the battlefield would be damaged on the strat map, but I thought this was just copied from Medieval 2 where that statement actually made sense.

I thought this because after such a battle the fort never showed any damage on the strategy map, only the other city buildings that are always damaged no matter how one takes a city. (This is totally illogical and should be looked at by the developers) Anyway, I repaired the city buildings, and thought no more about it.

Maybe 5 or 6 turns later, the battle option screen popped up saying I had an opportunity to intercept two little dinky partial enemy units with my forces stationed in this very fortified city. I guess these morons were going God know where, and decided the best route was through my fort.

When I get to the battle, I notice that the section of wall that I blew out when I took the city previously was still missing. Of course, it is actually is easier to defend such a fort in Empire because rather than trying to climb the walls the enemy will try to come though the narrow gap.

Still, as far as I can tell there is no way to repair damage to a fort and it just seems odd that they can not be repaired like any other structure in the game. It's not a huge issue since forts don't seem to change hands numerous times like they used to do in Medieval 2---especially those in the Holy land. Sometimes it seemed like I took and lost Jerusalem every other turn---either to those nasty Mongols or the even nastier Timurids with their elephants equiped with autoloading German 88's.

Cheers

On Retraining of Land Units
On the delay in retraining land units, I've posted that as a bug in the bug thread. I'm not sure if your hypothesis is right about the reason for the delay, nor am I sure about the idea that the money isn't deducted until the turn the retraining happens.

What I think is more likely is that it was a conscious decision to make retraining of land units take 2 turns instead of one when a) the unit is in the field or b) when the unit is in a city that doesn't have a functioning barracks. This, as opposed to the fact that ships get refitted in 1 turn, but only when they're in a functioning port. That feels more likely, but I can't say for sure because I've never tried to retrain land units while they're in a city with a functioning barracks. I'll have to give that a shot.

I also think it's a bug about how you can't get your money back if you choose to cancel the retraining after the turn when you initiated it (before it's actually happened).

On Repairing City Walls
This would be odd. I can't confirm or deny it, since I never use artillery and so I never damage any of the forts. I usually just auto-resolve most siege fights. But if the walls get damaged, they should show up as damaged in the campaign map view like other buildings and you should be able to repair it like other city buildings.

I had started to reply to this thread about 4 hours ago before i had to rush out, but what i was going to say is that i don't think the money gets re-added to your treasury on the turn after clicking retrain. As far as i know, units take 2 turns to retrain, and i've never had any problems with them not retraining properly.

I have discovered that if you click retrain, for example, on a unit that has 100 men left out of 120, then that unit gets into battle before being retrained and loses another 20 men, then when it finishes retraining it will only retrain the original 20 men you told it to, not the extra 20 men it lost in the battle after you clicked retrain.

I don't think that's a bug though, just something i've noticed.

In regards to losing funds when retraining, that's actually a very annoying bug. Some of the retrain logic must be missing code lines as a unit that has gone through an end of turn battle and taken some losses and you then cancel its retraining, you almost (yes, almost, not always) always do not get the funds back even though you should.
Similarly, retraining a unit and then disbanding it on the spot does not give you back the retrain costs as you would have if you first cancelled retrain, and then disbanded.

Re walls, its yet another bug that walls cannot be damaged on the strat map, but will never be repairable either even when damaged in battle. They stay permanently damaged even 10 years on. THe only way to repair them is to tear them down completely and rebuild from scratch.