1. Can I use tapes produced by HP in IBM LTO drives?
Yes.

2. Is it supported by IBM?
Yes

3. Does anyone do that? Does it work?
Yes.

I've had good luck with Fuji media, and it's fairly inexpensive.

The only cross-compatibility issues you may have with LTO is the cleaning
cartridge. If you don't get the universal cleaning cartridge, make sure you
have the manufacturer specific cartridge for your drive brand. The reason
for this is that the brand-specific cleaning cartridge uses the chip memory
in the cartridge for tracking the number of cleanings the thing has been
used for.

--paul