1) Towards the mid-game do players usually end up picking a tech route and ignoring part of the tree? I've sprinted forward toward some naval technologies because I'm playing a game on two continents and have begun an attack on a civilization on the other land mass... but I'm worried about ignoring some earlier tech items I skipped, still don't have Education for example.
People do beeline certain techs frequently, but its rare that naval forces are going to be pivotal when fighting AIs. Education in fact is one of the most commonly beelined techs in the game as it gives an important national wonder (Oxford), opens up the very useful Liberalism and Economcs techs and is needed for numerous important later techs (Communism, Assembly Line, Corporation)
2) As soon as I attacked this other civilization I began getting bombarded by Airships... Beyond my confusion about their presence at this age in the game I also can't see them or fight them in anyway. Are they completely un-attack-able until I get air units or something? They don't seem to do much damage but it could build up over time and really hinder this attack.
Airships are available at Physics and can cause a maximum of 20% damage to a unit. They are extremely useful despite the apparently weak damage.
Air units cannot be attacked directly, they must be intercepted by another unit while the air unit is attacking. Fighters are the most effective method, but numerous ground units have an intercept chance too, including Sam Infantry, Machine Guns, Anti-Tanks and Destroyers.
3) I've noticed that when you dedicate all of a city's production to Culture, Research, or Gold that output is unaffected by bonuses like Banks, Markets, and Library's... do players use this feature frequently or do they generally just continue producing units from all cities?
They are affected by hammer multipliers instead (forges, factories, coal plants).
Personally I build Wealth at some point in almost every game I play, and Research in many games too.
Research comes a little earlier and its main role for me is to get me to Currency, and Wealth I use to raise my science slider midgame.
The reason being that while the Wealth isn't boosted by banks, the gold produced will fund commerce based research that will benefit from Libraries
.
Building Culture is a very niche use, only likely to se use for speeding up a culture win or getting a border pop.