[2019] Is there any exhaustive resource of POEs game mechanics?

The rules is not "all increased modifiers are additive with each other" - as a trivial example, increases to armour are not additive with increases to, say, fire damage, because they are applying to different things. The rule is that all "increased" (and "reduced") modifiers to the same value are additive with each other.

The damage of a weapon item, and the damage of a player using that weapon, are not the same value.

A local stat granting increased damage to a weapon is addtive with other modifiers to the damage of the weapon - multiple such modifiers on the same item stack additively. They are all affecting the base physical damage the weapon has from it's base type. The final result of applying all such modifiers provides the total damage of the weapon, which is displayed above the mods (as noted elsewhere in the thread, if a weapon's physical damage is modified it's value will be displayed in blue to show this, while elemental and chaos damage are colour-coded by damage type, as they are always modified if present, since weapons only have physical damage as a base).

When you equip that weapon, it's total damage becomes the base damage for your attacks. Added damage on your character applies to it, and then increases and reductions on your character can apply to that value, which is not the same value that the local modifiers on the weapon were already applied to, although it does depend on that value from the earlier calculation. Both kinds of "increased" modifiers are additive, not multiplicative with other "increased" modifiers affecting the same value. They fundamentally cannot be additive with each other because they aren't applying to the same thing.

Similarly, increases to damage taken by an enemy are additive with other increases to damage taken, but not with increases to your damage that you try to deal to the enemy, because those are different values - the result of you calculating your damage is mitigated by enemy resistances and armour, and the types of that damage potentially modified, to work out the damage taken value.

That is not correct. Those are restrictions to what kinds of values those modifiers will apply to.

For example, the damage of your Fireball spell is Fire Damage, but not attack damage and not bow damage. "increased fire damage" would apply to it, but "increased attack damage" or "increased bow damage" would not.

But if you also have Burning Arrow, that skill will deal (by default) physical damage and fire damage (converted from physical). The physical damage is attack damage and bow damage, so both those modifiers would apply to that value (additive with each other), but the fire damage modifier would not. The fire damage would be affected by all three, so all three would apply additively to the value of fire damage dealt.

Practically, 100%, but technically neither. You cannot evade, so no chance to evade/chance to hit value ever gets calculated in the first place.

This is distinct from just having no Evasion Rating, which would not prevent you from being able to evade, but would mean the calculated chance to evade would usually be 0%. In that case the enemy chance to hit is 100%, and if they're blinded then that would affect that chance, which inhernetly brings up your chance to evade.

There is no concept of local damage conversion, and adding it would introduce a huge amount of complexity and unintuitive interactions to the system, and remove part of the point of using conversion mechanics in the first place (modifiers to both types applying - because a theoretical local conversion would be entirely on the weapon and only affected by local modifiers, and the player just gets the resulting totals for each damage type).