Questions.

[Raygereio]

I have the Alex executable but I could never quite figure out how to shortcut to it so that EB works and only utilizes the engine ( I don't want to mod, only use the engine ).

Use this shortcut:
RomeTW-ALX.exe" -mod:eb -show_err -nm -noalexander
Then grab the chat_filter.san file from Alexander/data and put it in EB/data.

That should enable you to start EB on alexander. Nightbattles have to be enables in the trait files and descr_strat.txt.

As for the OP's questions:
I noticed in Rome.exe, BI.exe and Alex.exe that the AI will by as much mercenaries as possible, limited only by money and the actual number of mercenaries available. (hard & very hard give the AI more money to buy mercs with).
I think the amount the AI buys is also affected by the ammount of factions the AI is at war with and how much units the AI can produce. For instance, I noticed entire armies of mercs with the Arche Seleukia (who is at war with pretty much everyone in my campaign), while the Iberians have very little (in my campaign they are at war with just 1 faction).

Edit; which is pretty much what Decius already said. I need to read more carefully.

I never saw an impetious unit charge without orders. I did read about people claiming to have seen it, so maybe it´s just really rare.

As for your intromovie problem; I had that problem once (while vanilla RomeTW, using XP; I think it had something to do with either windows media player or a videocodec), try using the -nm command in your EB shotcut that will disable all movies.