For the third point, check out the stickied Diplomacy Guide, it might have some usefull tips.
As for the popularity with the people. You can get traits that improve it (usually associated with conquering a lot of regions, which could give the 'victor' or 'conquerrer' trait), also getting more regions improve it, and lastly I think happiness also influences it. (So revolts are kind of bad)

Good luck with your campaign!