Fair warning: I am by no means an expert on playing as a pirate. I occasionally toy with it, but I much prefer playing as a normal empire.
1. You should expand when you've found a lucrative area which is too far off from your current pirate base to properly sustain a fleet in that direction. An example would be a small cluster with a few independent worlds that you can dominate, or a system with one of the superluxury resources (Korrabian Spice, Zentabia Fluid, or Loros Fruit). Having a base in the proper area means that your fleets are less likely to be crippled by slowly-accumulating damage from skirmishes with empires and other pirate factions (because you have a much more convenient center for repair work) and it helps safeguard a world you've put a lot of effort into corrupting or one which has something particularly valuable (a superluxury, or the only major source of chromium in three sectors, or something like that). The extra base also means you won't be as crippled if someone comes along and kills your original base.
Another reason why you might want to build a second base is that your original base is somewhere with no decent targets nearby, or with poor access to resources (e.g. if you spawned in a gas cloud outside of a star cluster, instead of over a gas giant in a star cluster). A third reason is that you're trying to make a push against another faction. Don't build too many bases, but don't be afraid to build a new base if it provides a convenient fleet station.
2. No idea.
3. The earlier you suppress an empire's growth, the safer you are, as a normal empire will almost always be able to out-research and, eventually, out-fleet your pirates. However, if the normal empire isn't in your stomping grounds, I'd tend to leave it be and just discourage encroachment. Remember that as a pirate faction, your direct competition is the other pirate factions, not the normal empires; tying up too much stuff trying to trim back a developed empire might be too costly, especially if the developed empire isn't distracted by wars with other developed empires or strong pirate factions.
4. I would generally prefer to take over independents, but if you can find an empire before they really get going (for example, if you find an Age of Shadows pre-warp empire before they get their spaceport up or shielded) then they're an acceptable target, possibly even a better target due to the higher population (but this hurts your ability to corrupt them, and also means that they probably have a decent number of troops available to blow up your facilities, unless it's a new colony that you're trying to take over). The planets of normal empires are much, much harder to take over than independents are, and it's harder to set up a decent support infrastructure for your raiders nearby - normal empires will typically build space defenses and ground forces which make raids, corruption, and hidden bases more difficult, they'll go after your ships and bases, especially those within their space, and you're just not in their league in military strength and economy if they've had time to build up, unless you've been doing really well.
I generally prefer to stay away from developed empires and take even minor protection agreements, and only really perform smuggling activities in their area. More strongly criminal pirate activities stay in the under-developed fringes - new colonies, poor colonies, areas devastated by warfare - when dealing with a generally well-developed empire, because you're just not going to successfully pull off a raid against a large space port, two or three defensive bases, and the local naval presence, and the more you tick off the giant, the sooner it's going to start swinging back.