To address your specific points:
1) Dunno, I hardly ever use random maps. The player-made maps look better and provide a more balanced MP game.
2) Not entirely sure what you mean here
3)
Scouts: The purpose of scouts is to detect troop movements deep in enemy territory, not near your borders where you get free intelligence. Use them to locate key enemy provs: forts provs, high income provs, low pd provs, etc.
PatrollingYou can detect stealth units via the Patrol command. Fast units and flying units get bonuses to patrol. Additionally, Province Defense above 10 has an increasing chance to detect hidden units moving through your province.
4) Nope. Probably should be there, but its not that big a deal since you dont care too much about individual soldiers in dominions. In case you were wondering, unit upkeep is directly proportional to the unit cost (1/15th for regulars, 1/30th for sacreds).
5) Nope. Put them at the front of your army as fodder
6a) Do you mean target spell casters? If so, that option was available in Dom1, but removed because it was far too powerful. As for squad orders "not working": squads normally try to carry out their orders as best they can, but orders and morale have a subtle interplay which effects the result. Too long to go into here.
6b) Too much micromanagement
7) I have this gripe also - Unfortunately no way to do this. Best bet is to just organize squads with like movement speeds and then arrange your formation appropriately.
8) Spellcasting AI same in demo and full game. It is not good, but given the amazing number and variety of spells available in Dom3 it does a tolerable job once you understand its limitations.
Q1) Generally speaking, all moves into a friendly provs occur before any moves into enemy provs. In a contested situation (where two armies attempt to move into each other provs) the result is random - tho it is unknown if things like army size influence it.
Q2) Independent strength is set at via the option when you create a game. Each particular province has some randomness as to troop makeup and amount (tho provs with powerful units like Knights will usually have less). Indys never move.
Q3) The most likely cause is Old Age (you are probably seeing this on your mages, right?). Healing wounds is possible via the global Gift of Health, the artifact The Chalice, and some units in the game which you are not likely to see in the demo.
Q4) No. Newly researched spells are available to all your mages anywhere, instantly.