Discussion about Heroes 4.

Look, if you had a class based on magical skills, then by maxing out even 2 skills out of 3, you'll become an Archmage. Usually, classes related to combat are prioritized. To change the class, max out the 16th skill in other areas; it will change. I wouldn't recommend maxing out all skills to Grand with a weight of 20, as the hero will either be an Archmage or a combat-related class, although there seems to be some class priority in such a situation, but I haven't found any information about it anywhere. Mostly, it's either Archmage, General, or Field Marshal.
In your case, if you have a weight of 15 in Scouting and Nature, the class won't change until the weight in other skills reaches at least 15. Why did you choose a Bard? It's not a very good class; it can cast mass luck on the very first turn, and it will still be a Bard. Also, it's better to increase magic resistance; it's better to max out melee and ranged combat, as the hero is focused on summoning anyway. Is Scouting your main focus? Are you leveling up a Thief?
It's better to make a Conjurer (Nature + Order magic) or a Demonologist (Nature + Death magic) – since you're playing with summons.

Added 14 minutes ago

Healing, mind magic, and morale don't affect vampires, but Holy Word does. However, they are still vampires, so why shouldn't a Lich, who becomes undead, also be able to drain life?

I didn't specifically choose a Bard; the idea is to allow the hero to fight effectively on their own. For this, you need Nature as a replacement for an army and a lot of experience to level up everything necessary. Stealth allows you to constantly accumulate experience, even if you can't kill these monsters yet, plus you steal mines, artifacts, chests, and other objects that enhance the hero, all of which give experience. For example, we're playing together, and right now, I'm 10 levels ahead, and without fighting, I have much better stats than the second player with GM battles. I also have powerful artifacts, like a bow with +50 attack or the Tiger set, which gives regeneration and constant dragon strength, which I wouldn't have achieved without stealth. So, the class is currently intermediate and will change later anyway, so it adds something, and that's fine.
I don't level up resistance because it's five unnecessary skills, and there's still a lot to learn. Also, magic resistance isn't required in every battle and can be easily replaced with antimagic if needed.
Melee and ranged combat may not be necessary in themselves, but they are needed to level up Combat, which greatly increases survivability, and this is relevant for a solo hero.
I'm not taking a Demonologist because I won't be able to maintain this class, as I don't need Necromancy, and because of the leveled-up Tactics, the class will be combined with it. And without a bonus to summoning, a Demonologist isn't very useful.

As for Liches and vampires, you're saying something strange. You've already been told that undead and vampirism are not the same thing. A Lich is just undead, and a vampire is undead with vampirism. It would be stupid to take this away from them; it contradicts the very logic of this unit, just as it would be stupid to give all undead vampirism. Do you think skeletons should also be vampires just because they are undead?