Leave firmware as-is, and you're unlikely to be able to change it anyway.
The drive is likely SATA --> USB. Whether or not it actually has SATA inside is a crapshoot. Some manufacturers do a direct conversion with a special board that goes directly to USB, others use a SATA-->USB adapter board inside.

As for what to do with it, that is up to you. You can hook it up to small form factor machines that don't have an optical drive to load/burn data, or you can just put it in storage to keep it on hand in case you need it. I find that they really come in handy if you have a laptop or mini-ITX machine that you need to load something on. It takes a slightly more modern BIOS to boot from USB-CDROM however.

From looking at pictures of that model, my guess is that the drive is actually a regular laptop drive stick inside a USB enclosure. Those USB enclosures generally do not pass through the brand/model information of the drive itself.

Those drives were used in HP servers (without DVD drive) to boot from DVD or CD. Mostly used for installing the operating system.

I have a HP mini laptop without DVD, and it's useful to have some kind of external DVD lying around...

The question was if I should keep it "as-is" or try to plug into my old laptop... but my old laptop is IDE and I guess this drive is SATA (although I've seen a Dell IDE laptop drive that was connected to a server using a mini IDE to SATA board, I don't think that my drive is an IDE one).

Also, I'm not really sure about that firmware information... in my computer the firmware revision seems to be RR01. The thing is that most USB HDD enclosures (or cable adaptors) that I have DO pass that information to the host computer, even if they do not pass other informations (like SMART values), and I know that HP usually puts their own firmware in drives. So I think that the information about the firmware is real, and it is a rebranded/reflashed drive from another manufacturer.

I would not try to make this drive an internal one.
External drives are nice, you connect it when you need it. Just curious, how often do you need to read/write CDs or DVDs in that laptop you mentioned?

If you want an internal drive, why not just get an internal drive? They can still be had, and cheaply. I think every enthusiast should own a USB optical drive, and USB floppy drive if your particular interests warrant one.

The general rule to flashing firmware is: Only if you must. If it's not broken, don't fix it. Most manufacturers recommend that, if everything's working fine, just leave it alone. The flashing procedure is not without risk, and particularly if you go off the beaten path and start experimenting with firmware images that weren't intended to be flashed to your particular drive. If HP uses LG as an OEM, and the drive in question is a 99% replica of a given LG drive, that is still a 1% difference in the design of that drive that could be critical when it comes to the assumptions made by device-specific firmware. Or it could be a different logo on the front bezel. You just don't know. Finding out could be a destructive process. For what benefit?