1. If you didn't start your TW experience with MTW:VI or Shogun, then maybe.
2a. Wow, good question. I've played RTW and M2TW, and I found those games to be rather lacking in AI intelligence. In MTW, the AI can handle the much simpler campaign map, and your decisions will be far more important - as someone said to me, you've gotta time that sucker just right. Timing is EVERYTHING. One moment you're planning a grand invasion of a neighbouring province, the next you're doing it, the next you realise why another faction has kept refusing to be your ally , and then you're in real trouble! Or you simply miss the window of opportunity to invade - cold wars are a feature in MTW, as your enemy will presume your build-up of forces is to attack them, so they'll fight fire with fire, and match you.
2b. The battlemap is definitely harder. The AI can make stupid decisions at times, there is never any preventing that in any game, no matter how well programmed. But in MTW, don't expect the AI to sit there as you shower it with arrows - it'll do exactly the same to you. You'll end up in skirmishes in some battles, only to have to then duke it out hand-to-hand once you and your enemy have run out of ammo. Some times, you have to go to the enemy, and they'll counter your army's heading by re-deploying, by turning to face you, or even moving elsewhere, and you'll then need to think of how to get at them at their new defensive position. Other times, they'll come to you, and will try to outflank you, divide your forces, etc. If the AI thinks it can't win a battle after an initial skirmish, it will run for the hills, it won't give you the chance to annihilate it.
3. Hmmm, been a while since I played vanilla MTW:VI, but for the main campaign, starting as the Danes in Early might be easy. Or playing as Sicily. Sicily has great access to creating trade routes, while the Danes have amazing Vikings which eat other armies for breakfast, regurgitate them, and eat them for lunch too - 'so two times devour' . They then go in search of other armies for dinner, and everyone has scarpered by the time it comes to supper.
4. I'd say stick with Normal difficulty for now. The worst thing you can do is play on Expert (even when you're capable of playing Hard...).

Oh, and welcome to the .org. Fine wine and fine women all around!