How should I prepare the site for a concrete step?
You're asking 3 questions, so I'll address them separately. In the future, please ask one question per post. 


There's no reason other than aesthetics and strength that you should extend the slab below grade. Since your step will be 6" thick, strength is not an issue. Use inexpensive substrate rather than making your slab 10" thick.  As far as substrate depth, that depends entirely on the existing soil. There's no magic number. The key is to remove all organic soil and be sure that what's left is thoroughly compacted. Water injection can help.  
Considering the small initial cost increase, I'd go with rebar in a 12-16" grid. It will provide more stability in case of cracks. For a slab that size I'd probably cut or tool 2 control joints on the thirds. 
If you attach the step to the patio and experience settling you'll end up with a slanted step and/or slab damage (rebar tear-out). I'd leave the step detached and 1/4" to 1/2" above the ideal height to allow for slight settling.  There's no reason to leave a gap or to install an expansion joint against the existing patio in this case. Expansion can occur away from the patio. If the new slab is flanked by other concrete, however, you'll probably want expansion joints at the ends.