Against the AI, the best strategy is to fortify one world that it likes to attack, use all the tactical slots. Make sure there is a phase jump distruptor. When they attack, your defenses and fleet will eventually make them retreat and the phase distruptor gives ou time to destroy as many ships as possible. Immediately after, attack the planet that the AI retreated to. Their fleet will be damaged and that will outweigh the home-turf advantage.
Against a human, do what the AI would do, attack the world where your opponent's fleet is. Only use a small portion of your fleet, and then retreat to a moderately fortified world. They will more than likely send a scout to see what is on your world, so make sure just the small and damged fleet is there. Once the scout is gone, move the rest of your fleet to that world (again, make sure there is a phase distruptor) and when the enemy attacks surprise should give you an advantage and the phase jump disruptor will make their retreat very costly.
This is a very generic strategy that works with all the races to different degrees.
1) fleets are not the best way to manage units, as they spend most of their time reforming. You can order the whole fleet to focus fire on a sequence of ships and they wont reform in between kills
2) When to get new capital ships is based on personal preference, but advent fleets usually bring out second and third caps earlier than the other races. Except on very small maps, the advent will usually start with a progenitor colonizer cap, the TEC with a Marza dreadnaught (in almost all cases), and the Vasari with the mighty space egg colonizer cap
3) Again, this is highly situational, if your enemy seems content to only attack frontline worlds, then you need no fleet presence at the first few planets. But a few long range frigates and support ships with disabling abilities will probably be enough to deter a small raid
4) Fleets are unwieldy at best, but you can (although it is a pain) go to the fleet management menu for every new ship and turn off the auto join fleet command.
5) A starbase will stop an AI dead in its tracks and will give a less experienced player a hard time, but to anyone with a moderate knowledge of the game, they are far too vulnerable to bomber strikecraft too pose much of a threat.
Keep playing and you'll figure out what works best for you, Good Luck!