1) Power and features. A flash with more power will, of course, allow you to bounce to higher ceilings, go through larger diffuse objects, and do daylight fill-flash at further distances.

Quick feature discussion:

• Tilt: Most models have this, save the lowly AF-200FG.
• Swivel: Most model shave this, except the AF-360FGZ for some reason. Tilt/Swivel are not a problem if you get a flash bracket or sync cord.
• Autofocus assist: Many flashes emit a cross hatch pattern to help auto-focus in low light. In general, this works much better than any AF-assist on a camera's body. It is non-disorienting, does not mess with exposures, and can work (depending on the flashgun) in extremely dark situations. Some even have an option to only AF-assist and not fire during an exposure, while some you can trick to do it (like the Sigmas).
• Manual: Some flashes only have a couple manual power settings which can be a pain. Others have more steps and go to lower powers. Quite for old lenses (particularly macros), and of course with off-camera flash. In addition, some do not allow manual in certain modes (like Av, Tv, etc).
• Zoom: The flash can adjust how concentrated its light is. Some flashes have less or more range, and some are more efficient at it.
• Wireless: Majority of the P-TTL flashes support optical sync, where any Pentax body can act as a master to trigger the flashgun, wherever it may be sitting. Only certain (Pentax) flashes / workarounds exist for getting Wireless HSS flash, however.
• High-speed-sync: Ability to use a higher shutter speed than the body's sync speed. Essential for daylight usage or any shots where the background is daylight. Say if you're under a tent during the day, it's either blown out background or dark people without HSS.
• Auto-thyristor: The flash has a sensor on the unit to determine the correct amount of flash to output. If you use older lenses that do not communicate aperture, you need this as P-TTL will not work on these old lenses or you are stuck in manual flash power mode. Supposedly there is a workaround, haven't tried it. Only the high end P-TTL models have this, and the AF360FGZ for some reason.
• Rear-curtain sync: Flashes by default fire right when the first shutter opens, as opposed to right before the second curtain closes. This means with longer shutter speeds, if your subject is moving, the flash will have exposed the earliest part of them. If this is a car driving in a line, it will be at the beginning of the line, as opposed to the end, which is generally not what you want.
• Recycle time: How long it takes to recharge the flash. Pretty important during events and high flash usage.
• Built-in bounce card: I guess it's nice to always have around, but its generally very small and you can't adjust the angle.
• Modeling light: Emits a burst of flashes so you can see what the shadows look like.
• Auto off: Some flashes don't let you adjust when it automatically turns off.
• Sync-port: Some have a port where you can directly plug in a sync cable instead of requiring a hot-shoe adapter.
• Stroboscopic mode: Emit a number of flashes during the exposure for creative effect.

2) Any in-production flash that says it supports P-TTL will not do any damage. What you are referring to are old flashes from long before P-TTL where the voltage may be too high. Generally, if you search, you can find out the voltage and see if it is compatible.

You can get old flashes for pretty cheap and many work great. The disadvantage is that they won't communicate with the camera via P-TTL. Many flashes have auto thyristor, or you can use manual mode. This means you can't just set whatever camera settings you want and have the flash compensate, but rather you need to set Aperture/ISO (flash speeds are generally so fast that shutter can be left to you to play with for creative effect) based on the flash's settings. My old AF280T (highly recommended for a cheap flash to play with) did seem to somewhat communicate in some modes, but I'm not really sure how well it worked.

IMHO, the best value flashes with most of the features and great power are the Sigma EF-530 DG Super and the Metz 48 AF-1. Having used the Sigma EF-500 DG Super (just less power than the 530) and the Metz 48 AF-1, I can detail differences if you'd like.

3) Speedlight is a name used by Nikon and Canon to name their hotshoe flashes. I will assume you mean strobes, which generally refer to studio lighting where they are hooked up to a battery pack or wall. These are bigger, have much more power for going through large umbrellas/soft boxes, and do not go on a camera. They often have faster recycle times and a model lighting mode. You can trigger them with a Pentax system using a sync cord or wireless gadgets like Pocketwizard or Cactus.

A good guide to Pentax flashes can be found here. It is pretty thorough, and he is in the process of updating it with any other differences that are pointed out.

A great flash photography resource is Strobist.