This one is easy. In one word,the answer is "Yes". Okay, I'll add to that. The whole point of jailbreaking is to have more not less than what your stock iPhone came with. So, if you jailbreak, you'll still be able to do everything Apple allows you to do on the iPhone, you'll just be able to do so much more.
1. The (bad) consequences vary depending on what you've installed. You may have Springboard crash intermittently, inability to use certain legacy apps and functions on the iPhone, heavy drain on battery, etc. The good thing though, is you have the best help resources in this forum, and if all else fail, you can easily go back to stock with a simple iTunes restore... And do it all over again. I always say there is a masochist lurking inside every jailbreaker.
2. Depends on what you like. It's much like the Apple Apps store - "Yeah, there's an app for that". The best apps seem to be those that improve upon what you already have on the Phone. Personally, and in no particular order, I'll pick Categories, SpotBright, SBsettings, LiveClock, Safari Close All Tabs and Winterboard (I'm trying to wean myself off of themes!). Of course, you need either Cydia or Icy to install the apps.
3. Yes, relatively speaking.
Reason to jailbreak? Because all you want from life is more! Frankly, there's no reason you should jailbreak. However, you have such an amazingly versatile device that can do so much more than Apple presently allows, it's such a shame to not tap into its full potential.
1. Downsides: Used to be lag. I haven't experienced lag with the latest 3.0 jailbreaks, at least on my 3GS. I can't vouch for V1 or 3G. It does void your warranty, but unless you experience a hardware issue that prevents you from restoring, taking it in for warranty work should never be an issue.
2. I'm assuming you're asking what program is best to jailbreak. It's not a clear answer. I've had great success with Purplera!n with my 3GS. It's by far the easiest, most svelte jailbreak I've ever experienced. Everything works.
3. Easy as pie. Takes about 5 minutes, if that, to JB with purplera!n.
Theming is big for a lot of people, but I think the 2 most popular apps are SBSettings and Backgrounder. The former allows quick toggling of commonly-changed system settings. The latter allows things to run constantly, even after exiting the program. These two apps are why I jailbreak, and I think many are in the same boat.
I would say go for it. If you run into problems, you have a rich resource of help here at this site...
A couple more that are hard to live without are MxTube, for downloading/saving YouTube videos and Elert and Tlert, which let's you respond to texts from within any app and read new emails without closing the app you are in and opening the mail app.
My reason for JB'ing: Intelliscreen. I happen to find this app indispensable. The ability to get a quick view of new email, SMS, weather, and/or news on the lock screen is, IMO, something that Apple should offer, a priori....but they don't, so I JB.