Understanding Sync & Transferring one account to another
Syncing is when you take two different sets of data (normally on two different devices or on one device and one online) and make them "mirror", or be identical to, each other. This way, you always have the most up-to-date version of that data no matter which device(s) you are currently using.

Many things can be and are synced, including a lot of different data from third-party apps, like Springpad (which syncs your notes) or Dropbox (a file storage service). However, for Google applications, I believe that it's just your contacts, gmail, chats (via Talk) Buzz posts, calendar, and documents. You can also upload and download photos from your Picasa account as well. However, I also think that Google has lots of other apps that do not come pre-installed on most phones, such as finance, which (I think) will sync with your online stock portfolio or the like. (I don't use Google Finance, sorry.) SMS is also only on the phone, though they have applications that you can download to backup your SMS to your computer.

No, other apps can use syncing as well, though I don't believe that they can sync to your Gmail account. Often times, these services have you register for separate accounts on their sites using your Gmail to sync with their service and their application on your device. For example, like mentioned previously, I use Springpad as a note-taking application on my Droid. I had to create an account on their site (though I could also log in via services like Yahoo! or Gmail) and it would afterwards sync with the application on my phone, so my notes on my phone are always the same as the ones on my online account with Springpad.

I think that you can add a Gmail account in your Gmail application on your phone. Afterwards, you'd likely be able to delete the old one. Though, you'd probably have to re-purchase or re-install your applications, as those are bought via your Google account. I don't believe it would delete your SMS as those are just on the phone, though it's always a good idea to clean your SMS out because they eventually start to eat up quite a bit of space unless you have them set to automatically delete as you reach a message limit. (For example, 200 messages)

For transferring data, there's a tutorial on transferring mail located here: http://www.consumingexperience.com/2007/09/gmail-transfer-all-emails-to-new-gmail.html (not written by Google, but the next best thing). For contacts, you'd just export them all from your online Gmail account and then re-import the export file into your new one.

Hopefully this answers your question and good luck switching!