It was my understanding that when the airport is in towered operation, we contact the control tower (CTAF) as we do in a lot of class D airspaces.
You have the wrong understanding.
At a Class D airport, the overlying radar facility (which may be a TRACON or a Center) is responsible for sequencing IFR aircraft only. VFR aircraft may call the Tower controller directly and will be sequenced by the Tower controller as necessary, given the feed of IFR aircraft they are receiving from the overlying approach control.
At a Class C (and Class B) airport, the overlying radar facility is responsible for sequencing all aircraft to the airport, both VFR and IFR (absent standing or case-by-case coordination to the contrary). This means you must initiate contact with the radar facility and follow their instructions; if they tell you to enter a left base, you should enter a left base, and not proceed to standard 45º downwind entry, for example!
If the tower is open and Class B/C airspace is in effect, the radar controller will tell you exactly when you should contact the Tower controller (and the frequency in use, if there is any possibility for confusion). You should not change frequencies without being instructed to. (The same goes for a Class D airport, if you happen to be receiving radar services from the overlying radar facility.)
- Am I miscalculating my zulu time?
No, you have it correct. 1200L = 1800Z; both the Tower and the Approach are open, and Class C airspace is in effect.
- Exactly when do I use ctaf vs. app/dep con vs. UNICOM in class C/E airspace? (Sometimes I've seen class E airports have CTAF and unicom frequencies be the same thing, and sometimes they are different.)
See this answer to the question "What is the difference between CTAF, UNICOM, and MULTICOM?" Note that your question can very likely be answered by reference to the Pilot/Controller Glossary, and you should always check the Glossary first if you come across a term you don't know. But as a primer:
UNICOM is a non-governmental service generally run by an FBO at an airport. The UNICOM operator can receive your requests for services (fuel, snacks, lavatory, etc). You can use this frequency at a towered or non-towered airport to request such services.
At a non-towered airport, the UNICOM operator can also relay the current weather, suggested runway, and known traffic operating in the vicinity of the airport—but they are not a controlling agency and do not issue clearances or instructions. Full authority and responsibility remains with the PIC to choose a suitable runway, make suitable traffic calls on CTAF, and see-and-avoid other traffic.
The Common Traffic Advisory Frequency (CTAF) is used by pilots when the Tower is closed, to self-announce position and intentions and, by listening to other pilots' announcements, build a traffic picture in their mind in the absence of a Tower controller. At airports without a tower, it is common for CTAF and UNICOM to be the same frequency; at airports with a part-time tower it is common for CTAF to be what would be the Tower frequency if the Tower were open, and UNICOM to be separate.
Pilot-operated airport and approach lighting is often controllable by clicking the mic three, five, or seven times on one of these frequencies, usually the CTAF.
When you are approaching an airport which has Class C (or B) airspace in effect, you must contact the radar facility listed in the Chart Supplement and shown in the magenta box on the sectional. If the Tower is closed and Class E airspace is in effect, you may contact the radar facility listed in the Chart Supplement to receive radar services, but this is not a requirement. See my answer to your fourth question below. If you are talking to the radar facility and the Tower is open, they will tell you when to contact Tower; if you are talking to the radar facility and the Tower is closed, they will tell you when you are "approved" to change to the advisory frequency (CTAF).
- When do I use RCO?
The RCO (Remote Communications Outlet) is a radio transceiver which provides on-the-ground communications capability at a non-towered airport to an ATC or FSS unit. It is used for relaying IFR clearances to departing IFR aircraft, and relaying IFR cancellations from arriving IFR aircraft. As a VFR pilot you would be unlikely to use an ATC RCO, but you might use an FSS RCO to open or close a VFR flight plan.
- If I'm operating between 0630Z and 1830Z, do I only use Minneapolis app/dep con for all communication and avoid CTAF since it is not in operation? Or, is CTAF related requests channeled to a different frequency?
Careful... if you are operating between 0630Z and 1130Z you would use the Minneapolis Center frequency for any purpose that you would normally use an ATC frequency when operating in Class E airspace, such as requesting traffic advisories or vectors around hazardous weather. There is no requirement to contact Minneapolis Center on that frequency, however, because the tower is closed and the Class C airspace does not exist.
You will continue to use the CTAF to announce your position and intentions and coordinate with other pilots, just the same as you would use the CTAF at any other non-towered airport, regardless of whether you had been receiving radar services from Minneapolis Center or not. If you had been, at some point (~10NM out) they would have issued you "Squawk VFR, change to advisory frequency approved" at which point your radar services would be automatically terminated and you would change to the CTAF.
NOTE that the current Chart Supplement (accessible from the FAA's digital Chart Supplement search page) is somewhat different from the Chart Supplement information provided in your question; the Class C effective times have changed and ZMP is no longer mentioned as the approach facility when the tower is closed. But having worked through the logic given the question's information, you can similarly look at the current information and determine that everything still holds—with the one exception that Omaha Approach on 124.0 is now the "Class E services" frequency even when the Tower is closed.