1) Even if the ROM installation doesn't delete all data and cache, it's a good idea to wipe it all before installing the new ROM. A new ROM running with the data left by the old ROM is like me walking on your legs - it's probably not too stable.
You back up everything before you install the new ROM.
2) No. You overwrite the old one with the new one. Usually you've installed a new recovery, so before doing anything else you do a nandroid (Android NAND memory) backup. That backs up the entire phone, as it sits. Then you can later do a nandroid restore of that backup to get back to where you were.
3) You didn't ask, but sometimes when you install a new ROM, your phone becomes a little piece of plastic, useful for keeping paper from blowing away in a breeze. Not often, not if you know what you're doing, and not if you wait until the hangover passes before you try. But sometimes ...
4) You also didn't ask this, but you know the warranty your phone has? And the insurance you bought, just in case? Install a new ROM and you can use them to wipe up the spilled coffee. At least, then they'll be worth SOMETHING. If the printing on the box the phone came in fades, it's not covered by the warranty if you put in a new ROM. Even if the carrier updates your phone over the air, and that damages your phone, it's not covered by the warranty. (I'm still fighting my carrier over that one. And I didn't put in a new ROM - their update made it look as if something had been done to the phone. But they forgot to tell me that I should fully charge the battery that night, because they were planning to send me an update and if the battery dies in the middle of an update ... it voids the warranty if the phone dies in the wrong way.)
