Do Cylons have an FTL radio?
FTL is one of the exceptions to the laws of physics that RDM has allowed in the show. However, for colonials we only see the FTL jump. When they want to send messages via FTL, they have to send them in a ship that jumps. The Cylons have a better jump technology, but can they also send signals via FTL without using a ship? Examination either they can do this, or they have always had ships just outside of range of the fleet, just about everywhere it has gone. Let's consider:
Cylons can transmit the full contents of their mind to a resurrection tank when their body dies. Boomer and a Leoben die on Galactica when no Cylons are near, yet make it. However, there is a range. Gina feels she will download to a distant Cylon resurrection ship and helps the fleet destroy it. These downloads happen quickly, not in months or years, so they appear to be FTL. Pretty impressive to have an FTL transmitter in the brain that can't be detected with a microscope.
Signal from Olympic Carrier
Think back to 33, the first regular episode. In 33, a Cylon attack arrives 33 minutes after the fleet jumps. At one point the Olympic Carrier fails to arrive, and there is no attack 33 minutes later. However, when it does arrive, late, there is an attack 33 minutes after it arrives. It is destroyed, and the attacks stop.
If the jump officer of the OC is a Cylon, then once she receives the new coordinates, she can transmit them by regular lightspeed radio to the Cylon fleet that is attacking, before jumping away with the fleet. Those Cylons could then follow immediately -- no need to wait 33 minutes. And on the jump that the OC didn't make, the Cylons would still have arrived, since this presumes they are getting the jump coordinates with ordinary radio at lightspeed. This is true even if you imagine the coordinates are sent to a fleet 30 or so light-minutes away.
However, the attacks come 33 minutes after the arrival of the OC. This implies instead there are Cylons on the OC, and after the jump they look around, figure out where they are and transmit that to the attack fleet using FTL communication, and that this whole process requires 33 minutes.
Another explanation is that the Cylons can track where the fleet jumped, but that this takes 33 minutes to do. However, this doesn't explain why the non-arrival of the OC resulted in no Cylon attack 33 minutes later. The attacks take place 33 minutes after the arrival of the OC, not 33 minutes after it departs, unless the last theory is true. In addition, it seems to be a general theme that the colonials believe they can't be tracked after they jump, or they would have been dead long ago.
The only other explanation that works won't please people -- namely that 33 was all a game, to test the fleet. That the 33 minute delay was artificial, and that they wanted the fleet to have to destroy the OC and kill their own people for some reason. In that case no FTL is needed, but you do need a compromised jump officer somewhere in the fleet (not necessarily the OC.) Colonel Tigh could set it up -- but he's not aware of his mission.
D'Anna signals for her documentary to be picked up.
D'Anna Biers makes a documentary with a shot of a pregnant Sharon. When ready, two raiders appear to pick up a transmission of the documentary and are destroyed, yet it does get through. Perhaps the raiders are able to transmit it in their download of their minds, or with superior FTL radios. D'Anna needed some way to signal them to get them to arrive on queue, which it seems would need to be FTL.
Tracking the fleet
The Cylons track the fleet on the path to the Ionian nebula. Six, when grilled, says they detected an unusual radiation signature from their mining ship. But that would still be something that moved at the speed of light. The Cylons are able to show up at a location many hours after the fleet left. Is the radiation signature a red herring? (If Six knows they Cylons have a superior but secret tracking technology, she would be highly motivated to come up with a cover story.)
Are they able to track where a ship jumped to, given 12 hours? That would be something brand new.
It is implied they track the fleet, even with the radiation signature fixed, to the Ionian Nebula. However, it is not yet established if the fleet that appears there is the same fleet that was following. Starbuck declares "It's gonna be OK."
Receiving communications from other base ships
In "Torn" the Cylons receive signals from the infected base ship. But how -- all its raiders are infected, so how would it send a signal via ship?
Sending messages via jump-ship is possible but very complex. To send a message, you must know where the other ship is in advance. You can't send a message to a ship out exploring, unless it sent a ship to you first to tell you where it is. That requires a constant exchange of ships to keep track of the location of every ship. Possible, but messy.
Just always knowing where the fleet is.
It's also a credible to suggest that the entire chase of the first two seasons, and the third for that matter, were a lie. There is a fair bit of evidence pointing to that. In this case, the Cylons could indeed just keep a ship near the fleet at all times, ready to receive ordinary transmissions and downloads of minds. This also implies "33" was a game, too. It does not explain Gina's desire to destroy the resurrection ship which is very far away to avoid downloading herself. (Her use of a nuke avoids that question in any event, one presumes even a Cylon can't download if vapourized in moments.)
Of course, many fans are not yet willing to accept the idea of the chase being a ruse, of the Cylons always knowing where the fleet is. But it's that or FTL radio, and even then, things like Bulldog's ability to find the fleet, and Leoben's prediction that they would go to Kobol are hard to explain if there was a real chase.
Update: Resurrection Hub
Much later we learn of a central resurrection hub, without which resurrection is impossible. There is only one, that moves around. Somehow all the resurrection ships must communicate with that hub, and it seems they would have to do it FTL, or we wouldn't be able to see things like Sharon killing herself on Galactica to move to a base ship.