i still haven't found the tech for archery as an empire player. and i'm 10 techs into conquest.

I'm going to pull a Captain Obvious and say they REALLY need to have polished this game more.

Empire has good things to. For example, you can research very quickly in war three (however it's called) techs that give two buildings that decrease training of troops by 25% (for total of 50%). And buildings themselves are super cheap. And both are buildable by level 1 cities.

Empire also gets very quickly housing tech that gives 50 population capacity per food.

Weapons of Piercing I believe.

 The thing about the Empire tree is that most of the techs are only likely to show rather than guaranteed. The guaranteed techs tend to be those primarily useful for conquest - allied races and the group techs. I suspect the intent is to encourage the player to start recruiting armies and dominating the land rather than trying to tech up.

The main difference, I believe, is that the empire lacks buildings that add prestige, making it nearly impossible to fully level cities in a reasonable amount of time.  This creates a lopsided balance as kingdom economies will expand much faster and leave the Empires in the dust.  That is, after the vigilant minion spam exploit which guarantees Empire victory is patched.

Not to derail the thread into another VM discussion, but the arcane doom ability literally allows you to destroy any practical army in the game on the first turn.  For more, see the "Summon Spy" and "Vigilant Minion too powerful" threads. 

Woohoo!  That is certainly great news!  I have been planning a massive balance mod as well, but I don't want to start until things have stabilized a bit and we know what systems we are working with.

But back to the Empire tree, if people have so many differing opinions on it, its very possible that it is balanced as is.  I, however, am pretty certain that once MP is enabled, people will notice a distinct Empire owns the early game/Kingdom wins the long haul dynamic.

About population boosting... while I have made a thread on prestige kingdom vs. empire (didn't see this one, but I also thought it seemed rather lopsided) there is one thing I've been considering, namely that empire is supposed to depend more on talented individuals than an educated people. This may also count for prestige - namely, royalty. Currently that doesn't work (They don't increase prestige in a city, as far as I know) but if that's fixed, then things may become more even.

Of course, perhaps empire should have a 'manor' or 'estate' or something building which gives a +100% bonus to any visiting champions' ability, wether it's a merchant, royal, or researcher.. the building would also provide a certain amount of population room, I assume. This could even be turned into a series of buildings.

Kingdom takes a lot of steps to get somewhere, but those steps are certain.

Empire takes less steps, but have to deal with random chance.  However, they unlock a lot per step.

That's basically how the research seems to run.

You can get warhammers with first war tech, if you are lucky with empire.

I believe this is only possible if you use a faction with the Archery bonus.  For Kingdom, Archery (Ranged Weapons) is a dead-end tech.  For Empire, Archery (Piercing Weapons) is on the main weapons tech line and a prereq for Smiting.  It's fun to research smiting within the first 10 turns of the game and create a unit type that will never need to be upgraded.