No, they do not require a truss rod. Some of the Banjoleles have them installed, but they aren't required.
No. Some less expensive guitars do not have truss rods in their necks. Any guitar that is more than a toy should have a truss rod, with out the truss rod if your guitar got into some moisture and the neck bowed,you would not be able to straighten the neck out.
You can't!
Yes
It's a long rod lodged up in the neck of a guitar used for keeping the neck of the guitar straight. The truss rod is used to allow the neck to bend either way in response to the tension of the strings. Without it, there would be no steel string guitars, the neck wouldn't be able to handle the tension of the strings. Many beginners think that adjusting the truss rod will lower the "action" or how high the strings are from the fret board of the guitar. This is not entirely true and it is probably more of a Nut and saddle/bridge adjustment that is needed.
Suspension, truss arch & truss causeways
The geometric shape used in truss bridges is the triangle.
Put many straws together to make it stronger
not quite. the truss rod will in fact reinforce the neck, but the bridge area can really suffer from high tension. not to mention the saddle nut and tuners. When a CF Martin guitar was custom built for this kind of versatility it used a totally different engineering and it was much more acoustic than classical. why ruin a guitar?
As far as i can tell there are 27 different types of truss bridges (i.e. Brown truss, Bowstring truss, Kingpost truss, Long truss, and Pratt truss). Hope this helps :D
In short you can do, but it's a very lengthly process and will cost you a fair bit of cash. Usually the way to do it (assuming your neck is deep enough to accommodate the truss rod) is to remove the fretboard, then route a channel down the centre of the neck under the board, install the rod with the adjustment nut at the headstock end, then reglue the fretboard. Though TRUSS me, it's a lot harder than I made it sound just then! I'd recommend taking it to your local repair place to get a quote and don't try it yourself unless you're a master router. If the problem you're trying to fix with a truss rod is that you're guitar neck is slightly warped, then a slightly easier option would be to get the frets out, plane/sand the fretboard level and then get it re-fretted.
It depends on the problem with your truss rod. I answered a question already on how to adjust the truss rod on a bass guitar. Search for "How do i adjust a truss rod on a bass guitar?" If your truss rod is broken or the threads are stripped search for "truss rod rescue kit". Before you buy it, read the details and watch the video so you know what you're getting into.