Regarding Lord Haart: I don't know why he is the only one in the editor's list. But you can do this, for example: take another hero and replace his portrait with Lord Haart's portrait.

I want it so that visiting a city is mandatory, but a global ban simply doesn't allow this spell.

Easy! :) Ban the spell globally, but in the desired city, mark the spells that should appear in the guild of mages. Of course, you can then check this through testing.

At the same time, I remember that in my old map, with land 1000, I didn't ban spells manually in each city, and various flying spells appeared there despite the global ban.

It cannot be as you described! There are four possible options:
a) at least in one city, it is specified that the banned spell should appear;
b) cheating by a leveled-up AI player (see the relevant topic);
c) if someone has built a Grail in the Conflux, then there will be all spells in the guild of mages, unless for this city any of them are banned forcibly;
d) a stupid, but real option that you might forget about: an artifact that gives a banned spell appeared somewhere on the map (if Flight is the Wizard's Hat or the Tome of Air Magic).
We would need to figure out what exactly your situation was while it was still fresh in your mind.