A quick check to make sure since the wording is slightly ambiguous, research progress keeps between checks right? So if you invest 500 into a technology and fail the 500 roll, and next turn you invest another 500, you get the 1000 roll?
Yes, but not in the way you mean. There is a base threshold that you roll against each time you invest into research. The amount you invest effects the roll you make, as well as how much the threshold increases by. The only thing to carry over is the change in base threshold. Note, this threshold is shared amongst all players. If you increase through research, it gets a little easier for everyone.
Also uh. How does the order of operations between players work? Especially far as recruitment and combat and double especially complex maneuvers involving multiple armies?
Like if you had something like this going on, how would it be resolved?
First, all mercenaries are hired, then all manoeuvres happen, then all combat happens, then finally all construction and recruitment happens. Thus in your example, each nation's attacking units will move simultaneously and will fight whatever units are left to defend the territory in question. In the case of an additional blue army entering the attacked blue region on the same turn as those red attackers, the new blues will arrive in time to defend.
A question: How would trade and caravans work for me as an island faction?
You'll need to stick your caravan on a boat to get it across multiple ocean territories, or make regular rest stops at coastal territories. Otherwise it's just like a land connection.
For a land unit to hop across a sea zone without a ship, does it require one or two moves?
Two moves.