Culture is almost never a game-winning mechanic, even against the AI... and Advent doesn't really have that much of a cultural advantage over the other factions.

95% of the time the winner of a game is determined by who has the bigger fleet (or starbase).

If you're having trouble killing the Easy AI, try this. Play as TEC in a 1v1 random small against an Easy Researcher AI, with Pirates off and Quick Start on. Queue an Akkan as your free capital ship, build 2 military labs, research LRM frigates, and set your homeworld's Rally Point onto your Akkan capital ship.

Queue as many LRM frigates as you can. Once you've built as many as your supply can hold, go up a supply level and build more. Repeat.

Your scouts should have scouted a good amount of the galaxy by now. Once it's built, send your Akkan towards the enemy, colonizing planets as you go. Your LRM frigates will be supporting your cap. (Remember to develop Civilian Infrastructure on your newly colonized planets ASAP, or you will lose a lot of credits to underdevelopment) Once you start running into your enemy, you should have 30-70 LRM frigates along with your Akkan. They will completely decimate whatever fleet the AI has and you should be able to steamroll their homeworld in well under an hour, even with no micromanagement at all.

What culture does is it provides a small boost to tax and extractor income at all planets under the influence of friendly culture. It also can cause enemy planets to turn neutral (the enemy loses ownership of the planet) if your culture is allowed to influence their planet for a long period of time. (But it's extremely easy to defend against culture. One culture station and/or a capital ship is probably sufficient)

That's all. Oh, and it can also provide some small combat bonuses after you do the (expensive) higher-level culture research.

Using culture offensively is rarely a good strategy... culture stations are expensive and are easily destroyed if a stronger enemy fleet warps in.

Pretty much.

Once you have the basics of the game down and are preparing to fight harder AIs like Hard/Unfair and above, starbases make your job much easier. But on the lower settings, LRM spam alone will do the trick, even in the hands of a new player.

I'd suggest learning to walk before you learn to run.  Brute force isn't the end of the road in terms of strategy, it's just the beginning.  Once you get a sense of what can be achieved by raw brute force and how to do it, you can start building more elaborate tactical approaches.

All factions require careful planning and tactics.  Not getting away from that one with any of them. 

With Advent, your biggest ace in the hole is the "repulsion" ability of your iconus guardian, which lets you literally throw around the enemy fleet like rag dolls.  Used carefully this makes retreat impossible for the enemy and can protect more vulnerable units.

My advice on that one is to get to the point at which you can reliably beat the unfair difficulty AI first. 

No one pointed out that advent is hardest race to play with since its slow to develop economy slow to grab neutrals (free extractors) and most ships require a lot of micromanagement to bring full potential out of them.

TEC is easiest to start from and vasari is very strong due to movable star bases.  

Upgraded Starbases with several repair bays can hold off all but the largest AI fleets. Human players of course would just build bombers and sit at the other side of the gravity well, but the AI will often suicide its fleets on your defenses. Only the TEC AI has decent chance of destroying a fully upgraded starbase with a good part of its fleet intact.

Once you get to the mid game diversifying your fleet a little bit can be a good thing. A small amount of fighter/bomber (two mid level Halcyons can be enough) support with a few defense vessels (advent actually have the best antifighter ship) can keep moderate amounts of enemy fighters somewhat thinned down and distracted. Keep a progenitor mothership and a guardian or two in your fleets to greatly increase the survivability of your "battleball".

It gets there, now that you know how to make your most basic fleet, you can begin mixing it up with more complicated ships. For the TEC a decent force of robotics cruisers are a must, and if you were struggling with some strikecraft flak support as well. Later game some carriers and a more heavy cruiser based fleet are completely viable, not the least because the TEC economy really takes off to be able to afford them. Sadly they don't have a whole lot in terms of strategic abilities like the Advent and Vasari have, relying instead on brute stats and powerful single target abilities to win the war of attrition if they don't overwhelm their opponents early.

Ah yes, i forgot advent have homing mines..   

 ... which don't explode sometimes so gave up on that tactic

Yes advent homing mines sometimes overshoot target and when they get out of range they become stationary again.

Easy to try is to move your capital straight into and straight on the other side of minefield at full speed. Some of mines that are a bit on the side will overshoot.