Can I automate city queues?

I don't think you can automate it, but you can certainly create a production queue from the city screen. Tick the Show Queue box and add items one by one. You then won't be pestered until the queue is empty.

Note that the "show queue" check box won't appear on the city screen if you are not currently producing anything.

Unfortunately no, there is no Civ3/4 style Governor feature. But, if you capture an enemy city you have the option to make it a "puppet" city, which basically means it uses a governor- the entire city screen is automated and unavailable to you- in exchange for lower unhappiness. However you can't do this to your own cities.

Barrylloyd is right about production queues. Also note that there are no governors in Civ V, unlike IV. That's probably the feature you are remembering.