Here's a problem I'm having with hard surfaces.

In picture 1, I have a polygon thats unsmoothed, and in picture 2 I have it subdivided. The problem I'm having here is when I subdivide, I lose the octagon shape. I've tried adding edges, but when I try adding edges all the way through, it adds an indention in my model which I don't want. I tried adding edges at just the corner, then deleting the center so it would form 4 sides, but when I do, picture number 4 is the result. So....I'm not sure how to get around this. Any suggestions would be nice right now. I'm having

As for the top part where the cavity is, I'm trying to sharpen that area to a nice edge also, but it's hard to keep it straight because it's slanted. I tried changing my move tool to object, so that the arrows would follow according to the angle of the plane, but it stayed the same. So' I'm a bit confused. I've spent a while trying to play around with it but it isn't helping much.