Why they are called Engineers

I thought you were asking why they are called engineers? Your theory sounds plausible, but yeah basically they are creating new life. There are 2 accepted reasons: 1. Some engineers were creating bio-weapons for quick eradication of a planet's life form. Basically breeding out all engineer-like species across the Universe. 2. Some engineers just want to create Life and polinate potential Planets. That's also why they are called or dubbed by Shaw as "Engineers" since they are building something. You can probably refer to them also as Innovators, Creators or whatever but the film dubs them as that, Engineers.

So, there are possible 2 types of engineers in PROMETHEUS, which is one is creating a new life and the other is for creating biological weapons that the crews visit the temple which actually turns out is some sort of military field of the engineers?

I would assume that, look how many different races and types of people with different beliefs are here on earth.

Yes, the attempt to create the perfect organism backfires wiping them out. But what was the perfect organism from their point of view? It certainly wouldn't have been an organism that wipes them out, contrary to Ash.

In the concept art, there is a pic of the mural with an engineer treating an alien like creature like a pet, or a subservient

That's my point, in the one mural an Engineer is beside what looks like a Xenomorph as if it's a pet or something. In the other mural, it is clearly a Xenomorph in what would typically be considered the christ pose. So, is this what they were trying to create by seeding all of the different worlds? Trying to seed enough DNA throughout various worlds in order to be able to create their "perfect organism"?