Just like the problem appears in the image, I want to make a face triangulated around all circles. Instead, a face is created that overlaps everything I selected. What its the technique to join all of these faces? I tried fill, bridge to edge loops, and make face, but it's not turning out how I want it to be.
This is something that cannot be done in one press of a button or a click of a mouse. You will have to go through and manually create the faces you are wanting. To get triangulated faces, try making them first with quads and then use a Triangulated modifier. Or, if this does not suit you, you can do it manually. If you think about why this is happening for a bit, you should be able to understand why you are getting these results.