1. Enemy hidden units :
A battle somewhere in South America, enemy only has a couple of units, one of them are natives who can hide in bushes. I dispatch the first unit quickly, then spend 10-15 minutes combing the field for the hidden one. Am I missing something here, or is this the way it's supposed to be ? How do I find those guys who refuse to fight, flee or at least show up ? Am I too dumb to be entertained by this sort of battles?
The HQ unit can never hide, so once you kill all the visible units, that will have included the HQ unit. I've found that, when hidden units have hid the entire battle, and are now the only units left, they either charge you or flee. If they flee, they appear on the map. If they charge, they stay hidden until they're in range and then they pop. In my experience, these hiddne units are often Native Bowmen. They can fire while remaining hidden too. So, to speed the process up, I move my army to where the enemy army started the battle and wait a minute maybe. The enemy starts attacking, maybe I just see one of my units taking fire or I actually see the arrows flying, then I just storm that spot. Usually though, the hiding units just flee once all the visible units are dead or have routed from the field.

2. Enemy army remnants :
I win a battle. Enemy still has a couple of cav units fleeing (about 10-15 men each) - then I have to spend 3-6 turns chasing them down because they won't disband ? I remember in previous games they did so when badly depleted. Again, this is not fun, especially when some 20-30 enemy soldiers roaming in your lands can lay waste to 2-3 towns per turn.
It is still true that if you kill the vast majority of an army, even if some remnants of a very few units flee the map, the army on the campaign map will be destroyed. The army only continues to remain on the campaign map if too small a number of men and/or units were wiped out during the battle. As others have said, I usually detach my cav units from my army stacks at that point to pursue the remnant AI stack.

3. Naval battles :
They're pretty to watch, but degenerate in an utterly uncontrollable mess. I tend to get beaten when I expect to win, and don't get me wrong - I don't consider myself a tactical genius, but I'm at least competent after 10 years of TW. Example : small battle, me -2 ships, enemy -1 ship. I demast them quickly then move to its stern and start alternating broadsides. 10-15 salvos later, almost no noticeable effect. I move my ships slightly ahead, the enemy fires exactly once and routs them both instantly.
If you had 2 Sloops and they had a 3rd rate or something, that's possible. Demasting them is still the best option. Simply immobilizing them tends to make them surrender. If not, moving to the bow/stern and firing down the length of the enemy ship is the right thing to do too. You can try to sink them with round shot, but if they're a tough ship and you're a little one, that could take a LONG time. You can try to destroy their guns, but that usually requires round shot fired broadside rather than down the length of the ship. The next best thing would be to fire grape shot down the length of the boat to kill the sailors. Once their numbers have been reduced a lot, that'll make them surrender too.

4. Artillery control :
Sometime they won't fire (enemy is at point blank range, standing still). Other times they do, smoke and bang and all, but NO DAMN CANNONBALLS. Yet on other occasions, they yell something like "Open Fire !" (with funny Dutch accent), but that's all I get. And other times they fire at absolutely NOTHING. For minutes on end, if I let them. And where are the pretty target markers from previous games (shift key)? I need them badly, because I don't let my arty on fire-at-will since I've seen them obliterate half my army by ignoring juicy targets standing in front of them to turn their cannons around and fire canister along the line towards some routing cavalry.
Cannons suck in ETW. The volume of fire they can produce, and their accuracy, are both too poor to be worth their stack slot. In some very rare situations they can be effective, like guarding a sole breach in a fort wall through which the AI will funnel all their troops. But in the open they're pretty useless. I never us them. A unit of Line Infantry will always kill more than a unit of artillery (unless you get very lucky).

5. Houses :
Enemy loves them. They get holed up inside, just because they think it's a good idea when I have artillery aplenty. Really, are they any use at all?
They grant a defensive bonus in shooty fights. But you're right, they're rediculously dangerous if the enemy has artillery. In addition, if you send your infantry in to storm the building, they'll always get the 'attack enemy in the rear' bonus. Since I hate artillery in ETW so much, I usually just storm them with 2-4 units of Line Infantry or Grenadiers.

6. Walls with cannons and soldiers on top :
As above, what's the point of having them when cheap & reliable artillery is available right from the start of the game? The only thing they add to a siege is a boring few minutes on fast forward, while my cannons blow them to oblivion, and some smiles as the clueless defenders plunge to their deaths when the wall collapses.
You're right, they're pointless. Since every infantry unit has grapling hooks now, artillery is unnecessary. The cannons are also pretty weak/fire too slowly to be a real deterrant. Neither the soldiers nor the cannons can fire straight down, so just rush to the foot of the walls and you're safe. Or, since you like arty more than me, you can just continue to bombard them to smitherines.

7. City ownership after battle :
I lay siege on enemy city. Big army inside, so I wait. One turn left to surrender, ally decides to "help" - they move 2-3 units in and assault begins, with me as reinforcement. The allied army rushes to the walls, gets promptly destroyed and routed before I even had all my troops deployed. I carry on with the battle and eventually win, losing half my army in the process. The ally gets the city. Why the hell did THEY get it ? I was there first, and last, and did all the work. Absurd.
This has not been what I've experienced. In my experience, it doesn't matter who starts the fight, but rather which army has the most troops left when you get back to the campaign map. Then again, I have practically never gotten any support from my allies, so I think I've only had maybe 1-3 co-op city fights since the game came out. Maybe I've missed something. I guess the logical thing is for the instigator to win the city, regardless of which army is bigger at the end, but laying siege should count as the instigating action, not just who starts the final assault.