Wars: do what you want IMO. If you feel like you're winning, feel free to press the advantage; if you're not, go ahead and make peace (but, remember, we're getting war happiness from them I think, so for the most part, default should be war).
Cities: make slaves from captured cities if possible. Once that's done, I think more units (w/ barracks first?) is fine, I'd treat them like you would a normal city of ours. IMO we should make a few regular workers from cities close to the capital, to merge as soon as we get Shakes.
Research: Finish Democracy, then Free Artistry as fast as possible. Capital should swap to Shakespeare's as soon as possible.