I'll break this into bits for an easier read. I;m sure you're going to like the Hero. The hardware may not be the latest, but it's more than sufficient to drive the phone.
1. I'm trying to define the term "ROM". In conventional terms this means Read Only Memory and I'm familiar with this. But when people talk about installing a new "ROM" on their device are they speaking of just installing a modified version of the Android linux kernel and OS? Is there any actual flashing done in this procedure?
You're on the right track. Think of it as flashing the bios on a motherboard. That's the whole purpose of getting root. You need to flash the ROM of the phone so that it will look for an update in a different location. You point that direction to the sd card on the phone. From there you can load anything that you tell the phone is an update. Only root can send the command to do this, so exploits are looked at in the kernel that's running.
They call them ROMs because they are in the read only memory in the phone.
2. If one was interested in installing a new "ROM" on their phone, how can I backup my factory one? I understand that if I root my phone and install my own "ROM" that I'm voiding the warranty. So my concern is, will I be able to restore everything back to factory and make it impossible to decipher if my device has been tampered with?
Yes. The factory software has been recovered and is archived in quite a few places online. Im sure xda has it hosted. You also have the option to do your own backup as well.
3. The main reasons I am interested in tampering with my phone are because it is a) sluggish and b) full of apps from Sprint that run which I don't want...things like the NFL and NASCAR apps. Which "ROM" would you recommend installing should I want to improve the performance of my phone and get rid of unnecessary apps?
If that's all you need to do, you can do it without changing the whole rom. Since you're root you can swap bits and pieces of the code as well as have access to the file system. Write access

A rom is basically a rewrite of the os. So much has been done and combined that it's easier to use a rom update. Root has RW on the file memory, but they're called roms anyway. Go figure, it's the interweb. For myself, for now at least I'm running macados rom as it's the only one out, and it does have some great features. I've done a few other tweaks on top of it, like removing some sprintware and fixing a few os bugs (tcp timestamp error and the renaming as package name bug). I like "new" and will probably end up trying a bit of everything, as a full backup and restore utility is built into the recovery image I flashed.
4. Being familiar with Linux, I know that any tools which allow the OS to run in "root" mode are dangerous. Mainly for the security holes they create. Is it really worth this compromise to speed up the phone and customize it? Once rooted, can I install a new "ROM" then unroot the device so it is again secure with the features I want? For that matter, once you root your device for any reason, is there a guide to unrooting the phone again? My impression of the term rooting means changing the system partition from being mounted as a read only mount to a read-write mount. Is that semi-accurate?
I'll be honest instead of tactful on the first question

You're root. You have to know what you're running, if you can't trust your judgment you shouldn't do it. there, thats done lol.
You can unroot the device, but then how are you ever going to revert? Yep. You would have to singly hunt down an exploit in what you are running to change it back. Don't do that. Just use common sense and don't run random code. You'll be fine.
5. I understand that many people want to store their apps on the external sd card, mainly because they are natively stored in internal memory which will inevitably run out of space over time. I'm not sure but I remember reading something about creating ext3 partitions on the sd to accomplish this and that shortens their life etc... Why would the sd have to have the ext3 partition to store apps. Does this kernel not understand how to mount a fat32 file system?
The kernel can mount fat32, fat16, ext2/3/4 and swap. A script to mount an sd card with 0 as ext2/3 500mb, 1 as fat32 xxxmb, and swap at 32mb is built into a custom recovery image you can copy to the phone. It's a mini bootloader that does other handy things as well. I do recommend you do this, entering text in the terminal gets old quickly with no real formatting. And yes, I recommend you use ext2 as ext3 eats up sd cards about twice as fast. it's the journalizing. Swap does as well. The image only mounts a swap, you have to tell the kernel to use it.
6. I have read about dangers in possibly bricking your phone through some of the procedures mentioned above. Is that truly possible if you have a backup of your original OS somewhere? The only way I can imagine completely bricking your phone is if some flashing is going on and you are unable to flash the original image back to the phone. Can you tell me how dangerous this stuff really is?
It can happen. I've noticed that mostly happens to people who knew damn well it might happen, but had to know anyway...or people who couldn't/didn't follow direction very well and had no idea wtf they are doing. Just by the questions you're asking I think you would do just fine, as you're not seeming like either of those lol.
7. Last question. If I root my phone and maybe install a new "ROM", what to do when Sprint eventually releases Andriod 2.0 for this phone? Would I have to restore to my original image, download the update then reroot the device (if possible after the update)? Or am I stuck with what I've got (I can't imagine this but I have to ask).
Again, thanks! I look forward to reading your response!
You're stuck with what you have until it's determined that the exploit to root still exists (which isn't very likely...nobody hides that sort of thing) or someone figures how to crack the new kernel. Unless you flash a custom recovery image, you can't go back. You can count on lots 'o folks looking, buts that's it.
thanks for asking. This is stuff we all need to keep in mind.