Reading your posts, I believe something is unplugged or the hoses are not installed correctly.
Also, from your first post, when the car is idling, and you turn the AC, not sure if this is what you meant by heater, the idle will drop until the ICV kicks in and brings the idle back up. I believe nothing was wrong unless this was happening with anything electric, like your lights, radio, windows, which you stated. I would need more clarification if I was your mechanic.
Then when you cleaned the ICV and put it back the idle was erratic, this means the hoses are not on correctly or something like this as you have an intake leak or you damaged the ICV during the cleaning process. That is my opinion of course from working on these engines for over 7 years.
Now after theshop looked at it, it seems to be worse. Normally during these troubleshooting steps, things stay the same, might get better, but if something goes bad, you should be able to rollback what you did to return it back to the status quo. If it does not, then things are getting damaged along the way.
Another option is to light up a tobacco cigar, remove the valve cover vent hose, towards the front of the engine and blow that smoke in. Just get a good body cigar.