Heroes from different factions

I don't like starting skills of some hero from my faction. If I buy a hero from other available faction, will they have any penalties leading my army? Will my army suffer any penalties?

The only drawback I see - initial hero price.

There are a few penalties.

Morale loss

mixing creatures of different factions reduces morale of the entire army

From the wiki:

Army Factors

Basic Morale stat of a unit is +1.

Presence of friendly alignment units in army increases Morale by 1. Presence of hostile alignment units in army decreases Morale by 5. Presence of Might alignment units decreases Morale of non-Might units by 2 and vice versa. Presence of Undead creatures decreases Morale of non-Death units by 2.

So, if for example, you want a barbarian to lead your non-might army, you inflict a -2 morale penalty on your army. If you want a thief to lead you academy forces it's a -5 and if you want a death knight in your haven army, that's a whopping -7 to your entire army.

Spell selection

A towns magic guild primarily has spells from its own school of magic and a little bit less from the adjacent ones. The other two magic schools don't appear at all.

A list:

• Haven: Primary: life, secondary: order, nature, not available: chaos, death
• Preserve: Primary: nature secondary: life, chaos, not available: order, death
• Asylum: Primary: chaos, secondary: nature, death, not available: life, order
• Necropolis: Primary: death, secondary: chaos, order, not available: life, nature
• Academy: Primary: order, secondary: life, death, not available: nature, chaos

By choosing a caster hero of a secondary class, you do reduce your spell options and by choosing one of a not available class, you do have no options learning their primary magic school until you capture a different town. Getting a caster hero as stronghold is pretty uselss, as they can't learn any spells without another town of a different faction.

Conclusion

Overall, going for different faction hero isn't worth it in Heroes 4. The heroes have a miniscule identity in the game. The only thing is their class, which determnies their two starting skills. They have no specializations and no primary stat growth (which is the main reason going for somebody like Crag Hack in Heroes 3 is so popular). Also, there are so many slots for secondary skills, you'll never fill them, so even, when your hero starts with something weak, you just lose two skill points. The only times, where I might consider switching it up are for the Academies Lord class, as Nobility is fairly weak (but the advanced classes formed with nobility are often quite strong and you could just go tactics + scouting/order magic/combat as well) and when I deliberately want to go for a different playstyle, e.g. playing haven with nature magic.