How to get around triangles? Im very new to blender, so this is probably a very simple question, I guess thats why i haven't really found a solution online for it. Ive been working on other 3d softwares that just doesn't handle certain situations the same!

Basically my question is how to skip using triangles when working on a model. for example the screenshot ill be attaching, i have my base of the mesh finished, and then i wanna extrude a part of the mesh which will create triangles or actually in this case even worse, Ngons. 

Basically i used the knife tool to cut out the part of the mesh i wanna extrude, i thought about using loopcuts But that would create just so many more faces, faces i don't really need.
Personally, I don't trust the knife tool unless it's to do something very specific. It can make lots of irregular faces if used as a freehand tool. I'd rather stick to loopcuts and not worry about the extra faces.

Judging from your second screenshot, seems like you're trying to make some kind of piece/emblem from your current mesh (which is starting to look pretty weird). I'd recommend to make that part as a different object and then join or parent to your first object.