1. Is early archer rush viable? >>> It sure is. But you need to remember to have enough melee troops with the archers to keep them alive. And, the fastest way to take cities in the early game is warriors + battering ram + archers killing the city's actual health bar once the walls are down (warriors with a ram will take walls down REALLY quickly).
2. How much should i expand before war? >>> Maximum one city if you have to build the settler. Often I don't build settlers at all until I get to techs that reveal later game necessery strategic resources. If I do build a settler, I do it only after my troops are already marching towards their first conquering campaign. If you can steal settlers early on, I mean the initial settlers the AI has at the start, then you can expand freely. But unless you get some huge production bonuses somewhere, focusing on building settlers before military, is in 95% of cases not helpful in a domination game.
In the very beginning it's useful to make war just so you can kill enemy's units and thus weaken him even if you can't yet take his cities. This serves a triple purpose: you weaken the enemy, you gain XP for your troops AND you get to make that civ pay you money for peace.
3. When is the first good timing push to war and destroy a civ? >>> As early as you can. And the same holds true for the entire playthrough. The earlier the time, the weaker they will be and the more you can have choice on how to develope their cities ( so you don't end up with dozens of cities that are district capped so none of them can build industrial zones). But there is a difference between pushing for war and destroying a civ. Typically a civ with one city left is a good thing because then they can pay you money for survival. And they can build wonders and districts faster than you can - only destroy a civ when it's beneficial. That means if the last city is really juicy or if there just isn't any possible benefit you can get from the last city surviving. Usually just keeping them perma-paying peace deal GPT is better than them being 100% dead - and you even get less warmongering penalties like this - which actually does matter even in domination games until you get to industrial era, at which point you can just give everyone the finger.
4. What should i be focusiny on building early on (encampments?) >>> 1. Units 2. Monument 3. Builder 4. Battering ram. 5. Granary or campus depending on city terrain. Build a settler in between if you have a very very good expansion spot available - otherwise just take cities from the enemy.
If you build an encampment to train your first army, you're too late to benefit from the early wars that give you the biggest boost. Typically you should build encampments ready for some new, later era units that you cannot upgrade your current units into. So when you have to build those new units, your encampent will make their building and training faster. As far as districts go, I'd say do a campus first, then a theater district, only then an encampent. Exception: if you are in real danger of getting into an early two-front war, then do use the opportunity of building an encampment along with ancient walls so your capital can defend itself without need of your army which is conquering another civ while the other neighbor is having a go at you.
