I am dumb in this area, so here goes.
On the iPhone if connected via wifi, either via my home router or any hotspot, if I am accessing the web, or any phone usage, except calls, am I charged by AT&T?
You shouldn't be charged by AT&T unless you're making a phone call or sending a text message. Everything else should be unlimited. Browsing, E-Mail, Stocks, YouTube, all that.
Yes, everything is unlimited but text and calls. However, when you receive your monthly bill look at it closely. My last one charged me for data usage. In other words, really big bill. If this happens, call AT&T and they will fix it.