I've said that JF can research Arcana, it'll just effectively be a generalist school giving access to a very select number of spells from various other schools (Chaos, Sorcery, Light). Of course, that puts him entirely at my mercy as to what spells are even viable in that combination, whereas the tenets of the true schools are rather better determined.
You can win with money alone, but it's not cheap. Apart from going for the Morganesque capstone tech Megaproject victory (destroy the global economy), higher levels of diplomacy let you subvert troops and territories. That's affected by loyalty, though.
Your unification bonuses are tied partially to how easy that territory was to unify (e.g. unifying Icedale will garner probably a Tier I victory or less, unifying Villvale will probably be a Tier 3 or equivalent victory because of those green territories, and unifying Foul will be a pretty frigging high Tier victory because even though most of it's 'standard' territories, getting Foul North will require you to make war on the Old Empire) and partially to your current status and goals. Money is potentially less useful than Territories, but it really does depend how you use it.
Tips for Tech Research: Large sums of money at once, unless you're doing £500/turn and trying to build up the research base to improve your chances, give you a much better chance of researching a tech on that turn.