Can you please advise me on a good rush tactic, also how to Eco boom early with the Advent.
Early-game Advent vs TEC is just not favourable for you in any circumstances. You will lose early rush battles, and you will fall behind economically. There's a reason Advent is the undisputed "weakest faction" right now, you know. On the other hand, Advent's fortunes reverse in the mid-game and if you can just stay competitive until you get there, you should be fine.
Key to any fast-economy strategy is expansion. You want to grab as many colonies as quickly as you can, and develop them to bare minimum standards. A high loyalty asteroid with three extractors is arguably the best economic investment in the game; it costs very little to acquire but generates lots of revenue in crystal and metal (which can be sold for at least 3 credits a piece on the black market). You can get a lot of mileage out of your Progenitor Mothership here, since its colonize ability reduces the cost of planetary upgrades.
Establishing trade is a little tricky as Advent, but believe it or not that 3-lab requirement isn't your biggest problem. Your biggest issue is actually the 2-lab requirement of the repair platform. Where TEC and Vasasri can get their repair platform unlocked with a single lab, Advent needs to sink two even if they have no other military needs at the time. Quickly repairing your capital ship is important for keeping momentum if there are any large militias.
TEC's fast trade is nice, but you can often match it with delayed trade and focus on quick expansion instead. When you do phase in trade, try to get a long chain of trade ports operational. Avoid having to spend too much on logistics upgrades, and intentionally leave space open to be filled by trade ports later. If you can build a long chain, you can generate very large amounts of revenue with relatively few ports.
Above all else, stay lean. Pinch every penny and divert it towards your long-term goals: a more advanced military and a more mature economy. While it might seem convenient to build a hanger here or grab an extra tech there, this can quickly add up to thousands of credits which could have been diverted to higher-priority expenditures. It takes a bit of experience to get this down, and without specific examples of your playstyle (ie, a replay) I can't give you specific advice.
If you want to try a military rush (this is map dependent; particularly on more spacious random maps this is a gamble) your best opener is the Halcyon Carrier, which can deploy a lot of strike craft with its "adept drone anima" ability. Using multiple Halcyons for swarms of reliable strike craft is arguably Advent's only really strong opener. If you can avoid early combat (it seems your opponent is playing defensive) you're better off teching to higher-level units than trying to make due with Advent's relatively unreliable low-tech showing.
so the bugged Illuminator damage will still be there unless you update.
Oh, I didn't notice this...
Yeah, build LOADS of illuminators and rush hard. Those things will shred just about anything. They are bugged, though, so this is kinda cheating if you don't patch...