3. The probability of joining also depends on the hero's internal strength criterion, which is calculated in a tricky way (unknown). It is known that it definitely depends on the hit points of the hero's armies, the hero's Attack/Defense (including artifacts), and possibly on the distribution of hit points among stacks (many hit points in one stack is better than spread out).

I'd like to add regarding diplomacy.. I already wrote a bit about our research on this topic on HeroesWorld.. now I found what's here:

In Heroes 3, when joining, 5 factors are considered:
- hero's strength = sqrt ( (attack * 0.05 + 1)*(defence * 0.05 + 1) )
- hero's army strength / monster strength (Ratio)
- monster aggression level (generated when creating the save)
- unit bonus (number of identical creatures = 2, or simply if there are similar creatures = 1, if there are none = 0)
- diplomacy skill

There are detailed formulas, but who needs them anyway? ;)
and monsters have as many as 10 loyalty levels! Although in the editor you can only set 5.

I have written a lot in the school regarding Heroes 2, I recommend the thread author take a look...there is also about diplomacy: why you cannot consider attack/defense in Heroes 2, the way you can in Heroes 3, and that it allows moving troops across the map! and many other things.. logistics, navigation... a lot of stuff.
for example, here is one of my lessons for students:
http://offtop.ru/heroes2school/v1_478982__.php