Do the electrodes in the EEG headband put anything into me, like an electric shock or subtle information?

Absolutely not. The headbands we use have dry cell electrodes so we don’t even use conductor paste with these. They simply measure electrical activity in your brain.
If you are alive, you have electrical activity which jumps from nerve cell to nerve cell. The EEG translates that into visible waves. The waves you see strongest on the screen are the winning waves, the most active ones at that moment in your brain.

Will you be able to see my thoughts? Will you be able to see if I draw a “blank”?

No, the electrodes pick up how excited or calm your brain activity is, and even that changes from second to second.

How many sessions will we need to be able to do Mind Phasing at will?”

Could be one, two or three is usual.