Some big chunks of asphalt hit the front bumper on my IS 250 and there's a couple decent-sized areas where the paint chipped away (see photo). There's also a crack in the bumper near the smaller paint chip on the right.

Is this something a novice could attempt to repair? Or would it make more sense to pay a professional to fix it? Do I need to replace the bumper?

I just want to learn what my options are for this kind of damage, any help/guidance is much appreciated.

Check the pricing for a replacement. Often times that is the less expensive option.
Without the proper tools and set up, fixing this by yourself would be difficult.