I have this object which is a rectange object, and a face which I made in Grid Modeller addon.
Its one object, but I want to make it better geo so I can inset faces properly and create a beveled raised edge, around the whole perimeter.
How can I join these faces so I can get rid of the edges (marked in red) of the cylinder that trespass into the rectangle.
Prepare your rectangle geo to be welded with a cylinder, join them and weld vertices or make a bridge.
More longer way is to use a boolean union, which will create a lot of artifacts and unwanted geometry in planar areas (sometimes it can be solver easilly, sometimes not) , but you can use another boolean difference/intersection on top of that to cut a nice clean geo.
Im personally always prefer first method in such cases cause its a lot more faster.
Um… what if you were to delete the faces, delete the unwanted edges, re-fill the face and knife down the edges not forgetting to press Z to cut all the way through? 
Edit: Oop, didn’t mean to directly reply to your post, I was just adding to the discussion.
I remember is some cases it was impossible to easilly get rid of those edges. But i check it now and yeah it works. Probably the issue are more common for older versions of blender.
