Firstly, I would like to introduce myself. I am SecretlyMrsKirk, the secret wife of Captain Kirk (is there any other kind?

) But you can call me Beth.
Well Beth, you came to the right place. Well, actually I'm new here too...but...I showed up at the right place...
Shut up, I was going somewhere with this.
I’m twenty years old, a student, a writer, a rambler. My first introduction to Star Trek was through my dad, the biggest nerd I have ever known, so I’d always been aware of it, pretty much since I was a toddler. We would watch Voyager together while I sat on his lap. I still have fond memories of admiring Captain Janeway and B’Elanna. But I was never a huge fan; it was one of the things that my dad and I did together as father/daughter. No, it wasn’t until February this year that I started watching The Next Generation on CBS Action channel in the UK, and then The Original Series in April. Not telling you why I was so suddenly compelled to, but let’s just say a guy was involved. Ugh. Anyway, enough of that.
Well, always good to start, even if it's through infatuation.
1. What do the different coloured uniforms mean? Why are some yellow, blue and red?
Color is for division. For example, Kirk wears yellow (or gold as some call it) and that stands for the command and operations divisions. Scotty wears red, which stands for engineering and ship security divisions. McCoy and Spock both wear blue, which are for the sciences divisions such as...well, science and medical.
In TNG though, they changed this all around. Red is for command, yellow is for engineering and security, green is for medical (it was blue at some point) and science.
2. What exactly IS warp drive? How does it work?
Well, first off, to understand warp drive, you need to understand why they have it. You see, there is no way to push a starship at the speed of light. The reason is that it would require infinite energy to push your ship that fast. Even detonating entire stars behind you will not provide the sufficient energy you need to move that fast. Worst still, at the speed of light, it'd still take years, decades, and even centuries to visit nearby systems because the galaxy is just that big.
So, as a story telling method, they invented warp drive. Now, what warp drive does is that it reduces the mass of the ship. Once the mass of a ship is reduced, then the problem of requiring infinite energy is no longer present.
To compare, pretend someone tied you to a six million pound block and told you to run. Well, that's obviously impossible. You'd never move. What warp does is effectively remove that weight so you can keep going.
3. Can a transporter work between different planets? Or other long distances?
Hmmm, I don't think it can work between planets. They did that in Star Trek XI, but that was also science from even beyond the last time we saw Voyager. There are alternatives to typical transporter technology which allows for even light years, but the technology isn't safe for repeated use, hence it isn't used.
Typically, the most you can get is an orbiting ship, moon, or space station for transporter purposes. At least for Federation technology. More advanced species can beam light years and in the 31st UFP, Starfleet can beam through time and space across tens of thousands of light years.
4. What happened to Janice Rand? And why did she only come back for the movies?
Um, I guess she moved onto other projects? Aside from a few actresses and actors from the original playing new characters, few TOS characters were shown in TNG, DS9, and VOY, save for the really big characters and even that was a rare.
5. Does Pon Farr affect female Vulcans?
If T'Pol is any indication, yes it does.
6. If it does, do they have it at the same time as their partner?
It occurs every seven years, so as long as they're the same age, then yes.
7. Do they HAVE to conceive a child every time?
No.
8. What is a stardate? How does it work? Why is it used instead of normal dates?
It's basically just code for a regular means of doing the date. Similar to military time. TOS, TNG/DS9/VOY, and ENT all did their dates somewhat differently, with the last one actually keeping a modern dating system rather than the stardates.
Here's the info on that:
http://en.memory-alpha.org/wiki/Stardate
9. If there’s no money in the 23rd century, how did Uhura pay for the tribble in Trouble With Tribbles?
The problem with Gene's vision of no money is that he still likes people to buy things. This is one of many in a long, long list of things that were bought. Sometimes they don't have money and sometimes they do.
People have reasoned this to mean that the UFP doesn't require money for people to have a standard of living. Basically, most things in the 23rd and 24th century can be replicated and energy production has reached a point where people don't need to pay for it. You could live with internet, good food, comfortable furniture, TV, a car, and so forth without ever needing to do a thing to earn it.
Of course, this is countered by the fact that if you don't improve yourself (basically, give back to the community), you're a loser. Basically, they use social pressure to propagate their economy.
Also, take note that it isn't really the 23rd and 24th century that don't use money--it's Earth and its colonies, as specified by Nog that it's humans who don't use currency (sort of). All other members of the UFP may still have a currency and economy, even if it isn't required of them.
10. What are those cartridge thingies?
During the time, they were supposed to be future floppy discs. I guess you could just think of them as large USB sticks.
11. If Decker died in The Doomsday Machine, how the heck did he get to be in The Motion Picture?
That was his father. Decker is both of their last names.
12. Could you tell me about some medical-related gadgets and how they work? (This one is actually quite important for my fanfic)
Ooh, that's a wide field. I again, refer you to Memory Alpha:
http://en.memory-alpha.org/wiki/Medical_equipment
13. Why do some planets have numbers after their names?
Because it's THE FUTURE!
Nah, just kidding. It's the number of the planet in order from its location of the sun. So if a system has six planets, the closest planet to the star is going to be say, Rigel I. The third planet will be Rigel III and the sixth planet will be Rigel VI.
14. How exactly is the Federation related to Starfleet? (I feel SO bad for asking this!)
Starfleet is the exploration and military branch of the United Federation of Planets. It's basically their space compilation of the United States Military and NASA into one.
15. Why does the Romulan race have the same features as Vulcans? They’re not from the planet, are they?
The Romulans are a cousin race to the Vulcans. Centuries ago, the Vulcan race fought many wars due to their elevated emotional state. Then Sarek brought logic and pacifism to Vulcan. The Romulans were the people who didn't like that and so left on starships to live somewhere else.
16. How come Sulu’s daughter was never mentioned until Generations?
Really bad writing.
17. How come Kirk wears a green shirt sometimes? IS NOT GOOD LOOK ON MAH HONEY.
Because he always had worn a green shirt. The original yellow uniforms were actually green, but due to the lighting and cameras, they appeared yellow. The wrap-around that Kirk wore was actually just made of a different material, so it came up as green rather than yellow.
18. Is Kirk the only one who calls McCoy ‘Bones’?
Hmmm, not sure. Probably. Spock is rather formal and most everyone else calls him 'sir' or 'doctor'. Bones in case your wondering, is an old term for doctor. Of course, they turned that into a joke-reference for the movie.
19. If Saavik is a Vulcan, then why did she cry during Spock’s funeral? Is it really THAT sad? lol
Maybe. Vulcans can occasionally show emotion under extreme duress.
20. What IS the deal with the red shirt joke? I don’t get that.
In the original series, to show that a situation was dangerous, serious, or just to heighten the tension of the scene, they'd kill off an officer. Since security wore red, it often meant that they were the ones getting shot at and killed.