They don't advertise in anything but their local free gas station paper so no one ever knows. 

It should be fine to electronically sign it,  but yes you do have to sign it.   

One last thought if you do Uber as well, which I recommend you do, get yourself some of those large magnets that stick to your doors that advertise you are an agent.

Is it worthwhile to get the papers they advertise in?

I thought about checking out one of those deals advertise in billboards, etc about $1400-$1500 per slab of granite.

You'd want to consult with an attorney for the legality of such things in your area and also speak with a broker on the rules of self-advertising while hanging your license with them.

In 1946, knob-and-tube was still possible, but not as common.fuse panel versus breaker panel;electrical system of insufficient capacity for modern, electronic living;Plumbing:galvanized supply and/or drain lines.  

Perhaps one that advertises that they handle hail damage.  

Regarding your Apache Junction lease option, had you been advertising it off-MLS and someone contacted you, or was it just happenstance that landed the buyer?

The big direct writers(companies who only sell their own product with their own sales force) put billions into advertising.