By default in Enemy Unknown yeah.

Syndicate

One of the first, games I got on CD. Ah, the good old panic. Incidentally, what I loved about this game back when it came out is that it actually is a strategy game that had an explanation of who you are and why are you watching the game from above. In Warcraft, Red Alert, Jagged alliance... etc there was no in-game explanation on why you could have a bird-eye view on everything and be able to move units on one end of the map, then quickly scroll to the other end to do stuff there.

Here is the next one:

What's a good way of dealing with those necromancer wizards? They keep raising zombies from the corpses so towards the end I simply get overrun.

EDIT: oops, I meant native necromancers. Lizards come later.

it must be Heroes

Not sure which game you mean, but if it's Heroes of Might and Magic, then no.

bump?

More hints? Pretty recent. It's on GOG.

Eador?

Nope.

What is the genre? TBS?

A specific sub-genre of real time strategy.

Do you control a single character in this game? And if so could you describe him/her?

You directcly control only 1 character in each level, though in addition to that you control other aspects (buildings, spells...).
There are several characters to choose from and you can switch them inbetween levels (once you start a level, you're stuck with that character until you finish the level or quit). The characters include: a barbarian type fighter, an archer, a mage, a pirate, an alien (!) and a dragon.

Nope, that's not a real time game.

(I've redacted my guess)

I have a feeling that it should be easy to guess now but... I have no idea! Some kind of a hint perhaps? Or maybe question: is this game part of a series/games with similar universe?