[Optional static province resources?]

There is some logic to it, check out the following files:

ProvinceFeatures.def
feature_presets.def

In the feature_presets you can very strongly hint that the game should put a particular resource somewhere, although it's not guaranteed if the province already hit the ProvinceFeatures limit.

I suppose you could put the chances in ProvinceFeatures.def for everything at 0, and then manually configure the distrubution in feature_presets.def per province. Then you should get a 100% predictable map I expect.

[Does the AI always accept requests to Claim Inheritance?]

It's quite a complex decision:

 

	pros = 5 // a.k.a. peace points
	{
		pc_we_have_good_relation { base = 2; max = 30; pow = 0.5 }
		pc_our_army_is_weaker { max = 40 }
		pc_we_have_trade = 5
		pc_our_trade_level { max = 15 }
		pc_their_trade_level { max = 15 }
		pc_we_have_nap = 10
		pc_we_are_allies = 20
		pc_we_share_same_religion = 10
		pc_we_have_rebels {	max = 25; per_rebel = 5 }
		pc_we_have_war_exhaustion {	max = 50 }
		pc_we_have_too_many_wars { max = 50; at_war_base = 10; per_additional_war = 20 }
		pc_we_need_peace_time { max = 20; minutes = 20; pow = 2 }
		pc_too_many_global_wars { max = 20; num_wars = 20 }
		pc_our_authority_is_low { per_negative_point = 10 }
		pc_their_diplomat_skill_level { max = 15 }
		pc_we_are_their_vassal = 20
		pc_they_plan_invasion_against_us { max = 30; per_ally_province = 3 }
		pc_their_influence_in_our_kingdom = 30
	}

	cons = 50 // a.k.a. war points
	{	
		pc_we_have_no_border = 20
		pc_they_are_too_far = 50 { threshold = 3 }
		pc_they_are_our_vassal = 20
		pc_we_have_bad_relation	{ max = 30;	pow = 2 }
		pc_our_army_is_stronger { max = 30 }
		pc_they_rule_our_people { our_kingdom = 10; our_culture = 5; our_culture_family = 2; max = 30 }
		pc_they_rule_our_lands	{ per_historical_realm = 5; per_core_realm = 5;	max = 30 }
		pc_we_are_X_times_larger = 20 {	X = 2 ; added_realms = 2}
		pc_they_are_excommunicated_and_we_are_catholic = 20
		pc_we_want_to_liberate_rome = 100
		pc_they_hold_our_holy_cities_and_we_are_Sunni {	shia_control = 10; other_religion_control = 50 }
		pc_they_hold_Baghdad_and_we_are_Shia { sunni_control = 10; other_religion_control = 70 }
		pc_we_both_have_under_X_towns = 30 { X = 3 } 
		pc_there_are_our_loyalists = 10
		pc_they_have_rebels	{ max = 15; per_rebel = 3 }
		pc_they_have_different_religion = 5
	}

If the amount of peace points is equal or higher than the war points, the AI accepts.

[UnionQuests do not change the Kingdom's UnitsSet (in Kingdom.ChangeNameAndCulture)]

After my proposed change, the new special units DO show up on reloading the game. So in addition to the change in the OP, I suspect that UpdateUnitSets also needs to be called for every Realm of the Kingdom in question. That should solve it all!

[UnionQuests do not change the Kingdom's UnitsSet (in Kingdom.ChangeNameAndCulture)]

Well, that's at least part of the issue. The new special units still don't show up in the recruitment window, but at least the Kingdom's unit_types list is now updated properly.

[UnionQuests do not change the Kingdom's UnitsSet (in Kingdom.ChangeNameAndCulture)]

For example, if you do the Union Quest to reform Italy, you do not get access to the Pavise Crossbowmen that are defined for Italy in kingdoms.csv.

The bug is in the method Kingdom.ChangeNameAndCulture

Although the csv_field is properly assigned the value of the new Kingdom, the parameter unitsSetCSVKey still holds the value from the old kingdom. Then the method LoadFromCSV is called with this old unitsSetCSVKey value rather than csv_field.key, resulting in no change to the units at all.