Steve,
What you are doing is what we have done in past years on old buildings some I thought was a waste as it sat on solid rock, but we jackhammered out the rock and undermined the footers, 3500 footer mix is the concrete that I recommend and also use a vibrator as that works best (used on bridges) yes you footer should be 24" wide from what I gather you are doing, come up your pre-existing foundation at least 3" and when you go to pour your new slab drill 3/8" by 6" long rebar into the side of your new footers that will keep you basement floor from settling any, unless you floor is higher than you new footer which in new homes we put 2" of 3/4" stone over top of footer so that it doesn't nit to concrete and a expansion around the perimeter. Hope this is some help.
Joe~~
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