1.) You get favor points by performing well in games. When the game ends, it shows statistics for certain battle objectives, such as, most kills, kill streaks, most structures destroyed, etc. The more battle objectives you score highest in the more favor points you receive. Winning also gets you points, as well.
2.) You get gold from citadel upgrades, killing creeps, killing enemy demigods, and destroying structures.
3.) Mana, like health, is constantly regenerated. You can boost regeneration through skills and items.
4.) Your war score increases as you capture and hold flags. The more flags you own, the quicker your war score rises. Your war score allows you to buy citadel upgrades. As your war score increases more citadel upgrades become available. Leveling up increases your stats and allows you to invest more points into your skill tree.
5.) The more you play single player the more you will become familiar with the game. First player is extremely easy even on Nightmare, simply because the AI is horrid. Once you get a handle on the mechanics of the game, you can start to play multiple 'noob' games. Reading the demigod guides can help, especially if you aren't really familiar with a specific demigod. I recommend playing each demigod so you can understand all their skills and what their strength/weaknesses are.
6.) Single player will get boring real quick. Multiplayer is much more challenging as human players (well most) are much more clever than the AI.
7.) Just FYI. If you decide to play multiplayer and your computer is ancient, your system may bring down the game speed for everyone else. If this is the case, I suggest avoiding multiplayer until you get a new system (or heavily turning down settings to allow the game to run at a reasonable speed).
8.) You should upgrade the game to patch 1.20, and that should allow you to play the new Demon Assassin demigod. Oculus hasn't been released yet, but should be (hopefully) soon.