I should start out by saying that I am definitely a novice.
I've noticed a few things and developed questions because of those observations.
It's good to have you aboard! Keep in mind that everyone was once a novice and had to work their way through learning all this technical stuff like you are doing now. I'll get started before jumping into radio systems by providing a few links to some of the existing explanations of trunked radio systems we have.
Trunking Basics - The RadioReference Wiki - As it says, the basics of trunking, a general overview of what is happening.
Trunked Radio Systems - The RadioReference Wiki - A collection of links to other resources regarding trunking.
http://forums.radioreference.com/ne...d-forum/279839-radio-system-basics-video.html - A video covering the basics of radio starting from the radio and leading to trunking systems. About 21 minutes long.
As for your question, I will try to explain it the best I can based on my understanding of trunked radio systems. I may not be able to fully explain my answer (or sometimes explain incorrectly), so feel free to ask follow up questions and take other responses into consideration.
1.) Is the ARMER system a giant blanket of coverage? As an example, if a radio in a talk group half way across the state attempts to reach other radios in the talk group, must those radios be within range of the same site, or does ARMER provide a means for that information to be relayed to other sites where the rest of the talk group is present.
Your observation is correct regarding the blanket coverage, but there are times where there is an exception due to system radio techs setting up radio denials and such. ARMER, as any other big networked system, is able to route the call through its infrastructure to any other site that has a radio affiliation (a radio listening to that talkgroup on that site). Radios do not need to be on the same site to hear the same talkgroup as the system will work figure out and network the calls to the necessary sites with radio affiliations. It is important to note that a radio needs to be affiliated to a talkgroup on that particular site to hear the radio traffic, especially if you are a scanner user. The system will try to preserve the frequencies that is has and will not transmit a talkgroup if no radios are affiliated.
Now the practice of switching to a talkgroup from halfway across the state would probably be frowned upon by system managers, but that's a different topic.
2.) I noticed that some sites are assigned various frequencies. For example the site near my residence has seven assigned frequencies. One is the primary control channel, and another is the secondary control channel. What are the other five for? Are these seven listed frequencies the frequencies upon which communication is actually taking place, or are these frequencies just used for the sake of letting the radios know which frequencies to switch over to in order to communicate?
The other five (and probably the alternate control channel as well) are used for the physical aspect of communicating. Wireless communications still requires a frequency to operate on in order to transmit and receive messages, and not everything can take place on a single control channel frequency. Basically what is happening is that all radios (and scanners) are listening to the control channel in order to receive information that it contains regarding what frequency it should switch to in the event someone presses the push-to-talk button on a radio. Once someone presses that button, the radio (and scanner) will effectively be told that there is a voice grant on a particular voice channel (one of the 6 frequencies listed in the database) and that they should switch to that channel order to hear the transmission.
The idea of a trunked radio system is that you are attempting to preserve radio frequency resources by what I usually describe as "visualizing radio channels (talkgroups)." Instead of dedicating a frequency to a channel that you likely aren't using round the clock, you add it to a pool of trunked radio frequencies (channels). The idea is that you can organize yourself by having a greater number of talkgroups and operate on the theory that most transmissions that do occur are short and not active 100% of the time. This means that you can effectively have more talkgroups to switch to while using less frequencies as they aren't infinite in quantity.
3.) I pulled the FCC license for my county, in which the ARMER site resides... and the frequencies in the FCC listing don't match the frequencies for the ARMER site on the Radio Reference database. 1800 units were assigned frequencies in 300 unit blocks, for a total of six frequency blocks, and then six more frequencies were assigned to six individual repeaters... are these repeaters considered to be the ARMER "site" or is the site a single location, and the repeaters are acting in another capacity.
Most trunked systems operate as a duplex repeater system, so they require an transmit (classed MO - lower 800 MHz) and a receive (classed FB2 - mid 800 MHz) frequency. For an 800 MHz system, the transmit offset is always 45 MHz lower than the receive frequency. The database generally only lists receive frequencies as that is what used to be important for scanner users (not so much with the P25 systems).
If you are looking at a site license, you probably want to be looking at the FB2 repeater licenses. I don't know what particular site you are speaking of, but you can be seeing a simulcast site depending if the exact same frequencies are operating at multiple locations. A simulcast site is effectively acting as a single radio site with multiple repeaters broadcasting the same information at roughly the same time. This is another method of preserving frequency resources in order to cover a larger geographic area with the same frequencies. If the site in acting in this capacity, then this would explain why one would see the same frequency at different sites. The other reason for this is that it is that some ARMER sites are licensed under the same license for ease of paperwork and organization. This would be indicated by seeing completely different frequencies being assigned to different locations.
4.) Do the frequencies assigned to the 1800 handsets split into 6 blocks of frequencies get used for actually transmitting voice data, or do these frequencies just get used to communicate to the site, and then the site tells the radio which frequency to transmit over?
As mentioned above, a repeater system requires 2 frequencies to operate on. If you look at the 45 MHz offset, you can actually see that these frequencies are paired with those licensed to a repeater to operate on. This also ties into question #2 where a frequency is required to transmit voice data. The second part of this is if you are the one pressing down the PTT button, your radio transmits that request to the radio site on what I believe is the frequency pair for the control channel. At this point the site + zone controller figures out an unoccupied frequency for your site (and other sites that someone else might be using) for which you and other can use to hear communications. The control channel will then tell your radio the lower 800 MHz frequency that you will transmit on as well as tell everyone else the necessary mid 800 MHz frequency in order to hear the transmission you are making. One this process is complete, you will hear the little push-to-talk tone telling you that you are free to talk. All this generally happens within milliseconds.
In the event that the system is particularly busy, all the frequencies assigned to that site may run out. In the event that this happens, then there are no more frequencies that can be used for radio transmissions. A site cannot use a frequency that it has not been programmed to, only those licensed (for example, the other 6 frequencies on the site near you). Once this happens, a user will actually be denied from talking on the radio through a harsh sounding busy tone. Generally the user is attempting to make a transmissions should keep the PTT button pressed down as the system will put your voice grant in a queue as it awaits for a frequency to be freed up for transmission.
I hope I was able to answer at least some of your questions. Remember, feel free to ask if you felt like one of my answers did properly answer your question!