It's the second game of a series. There is a third game but it's not available on PCs yet.

Additional hints:

Buildings are the most important aspect of this game and are practically what defines the genre.
Cartoony kind of art.
You are chasing an evil wizard who stole a hammer from a your city, located in the desert. The native necromancers come in a later section. The lizards come yet later.

That's a hint each for gameplay, graphics and story. I'd be happy to post more hints, just tell me what kind of you want.

Kingdom Rush: Frontiers?

Yes.
The necromancers were a huge problem in Iron challenge of the volcano. You're limited to what towers you can use, and if you don't kill them quickly enough towards the end the zombies will just rush you. Unfortunately you can't direct the towers to attack any thing but (with few exceptions) the unit closest to exit, so they'll keep going for the zombies instead of the necromancer.

New one.

I need a few parts to build a student-like project that would grand me a promotion. Normally, I wouldn't bother too much but this playthrough is a bit different and thus I really need to finish said project fast.

Feel free to ask questions ;)

How many? Could you describe some/all of them?

Six of them. They look (more or less) like parts of a human body

At a more or less "magical" school/university/institution?

Indeed!

Discworld 2 (Ooooh, Chucky, Chucky, Chucky!) :)

(Totally didn't recall what "this playthrough" was referring to until I was certain already, but obvious in hindsight. Great hint!)

Sorry to disappoint you but it's not a correct answer. I don't remember Discworld 2 that good but were you supposed to collect 6 parts that look like a human body? Furthermore "this playthrough" hint is rather importnat. It means that normally I was taking it easy to complete this mission but this time it is very important for me to finish it fast.

Ooh, unexpected! I'm very much going off dim memories, but it did all seem to fit, particular with the magical university. (I think Hex caused some explosion which caused a timeloop? And I'm all but certain you have to collect various pieces of some kind of Frankenstein midget thing...) I'm wondering now if Discworld 2 was parodying whichever game you're referring to...

To check that last: Was your game published in 1996 or earlier?

No, it's a bit newer. And definitely Discworld is not anyhow parodying it :)

Why? Will something happen if you don't finish it fast enough?

Because this time I'm playing the game with a very specific and difficult party build. Finishing this mission will make me by far more powerful while in most of previous playthroughs it just made me better but it was not really crucial.

Is it an RPG then? Could you describe the setting a bit. I know there is magic involved so I suspect fantasy, but how about elaborating a bit?