Yeah, Harald tends to start wars he can't possibly win. He never builds enough units to match his enemies, and being the worst civ in the game doesn't help either. This is standard Denmark in my games.
I try to send out my settlers really fast to avoid being forward-settled, so most of my wars are either over territory, someone building a city right next to mine (need to maximize that land when you play tall), or because they took a ruin I was about to get.
I raze all cities I capture unless I'm going for a domination victory. The AI never places cities in the best location, which is really important when playing tall. Annexing conquered cities does mean that you start with more land, population, and buildings though, so either is a fine strategy. Razi g cities is just my personal preference.
Actually, if you raze a city and build another one, the social policy rate actually stays the same. The rate only increases once you build more cities than the maximum you had before, so the social policy rate won't rise once you build the new city.
Science costs work like social policy costs. The amount of science you need to complete a tech increases with the maximum number of cities you've had in your empire. It's not really noticeable unless you build cities everywhere you can. It's mostly there so city spammers like the Iroquois aren't able to complete the science tree faster than everyone else.
I would recommend getting the expansions sooner rather than later. It makes the game so much better, and it changes the mechanics enough to make playing with the expansions feel like a different game, especially with the complete overhaul of the culture system. It is definitely worth the increase in the learning curve.