Cement pool overhang patch or replace
I would chip away everything that is crumbling and patch it. Make sure that you get all the cracks knocked out and patch out from there.

Chances are that the patch won't match the surrounding cement but if you think about it, you'll spend maybe $20 in patch materials (more if you need the trowel tools) and if it fails after a year you are out $20 and no harm done. If it holds, great, but at least you have a year (or more) to save for a larger fix in the future. 

As far as leaving the rebar there or removing it, you should be able to leave it there with the proper patch cement. They usually have bonding chemicals in the cement and can bond to the rebar without using a chemical bonding agent. You may need to make a form for the underside or just mix the cement a little dry. Forms can easily be made from foam insulation (the pink sheets) available at any hardware store.

One more thing, when you patch, don't fill the expansion joints with cement, use duct-tape or weather stripping to keep the cement out of the expansion joint.