How many upgrades to fleet supply did you make? By that point, you should have at least the first upgrade to fleet supply (250 max supply, 9% lost income).

Two military labs should be enough to research the Repair Bay and its associated upgrades. These, grouped with Hangar Bays and/or Gauss Cannons work well against repelling Pirate raids, or at least considerably slowing them down.

As for your crystal problem, you should have at least 4 crystal extractors with the colonized planets you have, giving you around 2 crystal per second. Additional research would bump this value up 13%, or to 2.3ish crystal per second (unless you mean you researched four levels of crystal extraction, since each research subject has 2 levels - then its a 27% increase to about 2.5 crystal per second). If it seems you're constantly out of crystal, either buy crystal from the Black Market or reconsider where you're putting your crystal (research is notorious for eating up crystal).

Normally, you would want to have at least the number 1 fleet in military ranking. Even if you don't have the best economy, you at least have the military might to acquire resources to boost your economy.

You were wasting your resources on the crystal research. It would have been more effective to research metal extraction, then to sell the metal and buy crystal - I take you had 2x amount of metal extractors to crystal and metal extraction is cheaper to research. Little things like this you can figure out with some thought. Take some time to analyse the graphs at the end - they will show where you were lagging behind the puter.

You were wasting money on research labs and research. Research should only come slowly over time. Build some cobalts instead right away and sent them to colonize the galaxy with your marza. It really sounds like slow colonization and economic expansion are your doom at the time being. Take first a roid, then the ice planet, the neutrals are easier to beat in these and ice planets really help with their crystal and population.

Trade is not really worth it in the beginning. I'd say get 3 planets first, then build the lab to research trade, and build a tradeport on all the planets at once.

Well, sometimes it's not smart because of the scenario. If your 4 planets are terran hw, ice, desert, terran, then you can depend on just the planets for income, and trade is not worth it - rather keep upgrading the planets. If they are metal heavy asteroids and volcanic planets, then you need the credits so you can buy crystal, and suddenly trade ports will be more valuable.