1) Recommended is M - battle, and H or VH - campaign. Higher battle difficulties will make the A.I. troops overpowered, but it won't actually make it smarter. Campaign difficulty mainly affects how quickly the A.I. will take a dislike of you. Since the A.I. is programmed to dislike the player, you may want to chose a lower difficulty. VH also gives the A.I. an additional cash bonus.

2) For more challenging battles, I would recommend the adapted version of Darth's or Sinuhet's formation mod.

3) I haven't played alex.exe, but I found no difference between RTW.exe and BI.exe other than that the BI-A.I. is more likely to carry out naval invasions. This can be good, but I've seen my share of stupid, pointless naval invasions as well. For example: in my old KH campaigns, the SPQR persisted in landing undermanned stacks next to Corinth, even though we were at peace, they had greater threats, and couldn't hope to hold the city.