Concrete – What to use to fill a small HOLE in the concrete patio

I would be more concerned that your wire looks to be at the very bottom of the concrete, making it useless. Concrete is very strong under compression but very weak under flex. The steel is there to take the flex and should be about center of the concrete. Definitely use a concrete bonding agent and Ditra. The Ditra will provide enough of a barrier that the cracks should not come through. Personally I would not put a huge pile of money into tile considering it might end up cracking

It's been a long while since I worked construction, but I think I remember dowelling into concrete in a similar manner with a 1/2" drill bit and #4 rebar. We used a sledgehammer to drive the rebar pegs in. It MAY have been a larger bit, but I think I remember it being the same size.