I have made this object with a boolean operation.
My question is: should I draw new edges so that every face is a square or could i leave it that way having a smaller number of faces but 2 of them with many sides?

Attached Thumbnails

---

My animations

My renders

Your going to want to make all of those stray verts loops here is a post of what I mean. As far as I know your going to want to do this to prevent problems further down the road.

Attached Thumbnails

Ok, thanks

---

My animations

My renders

if it's going to deform or be smoothed then yes you'll need to make the faces 'squares'

i'm pretty certain though you can't add the edges after that boolean. maya will complain at you saying you can't add an edge that ends or starts at a hole.

---

that's a "Ch" pronounced as a "K"

Computer skills I should have:
Objective C, C#, Java, MEL. Python, C++, XML, JavaScript, XSLT, HTML, SQL, CSS, FXScript, Clips, SOAR, ActionScript, OpenGL, DirectX
Maya, XSI, Photoshop, AfterEffects, Motion, Illustrator, Flash, Swift3D