Awesome that you’re interested in ham radio!

What can I (legally) do with this thing without a license?

Listen, mostly. Baofeng radios are typically sold as “Part 97” radios (FCC lingo for “Ham use only and requiring a license”), although there are some models which are actually “Part 95” which would be GMRS/FRS radios. The GMRS/FRS radio model would require a separate license for GMRS, although that one is essentially an application + fee payment. It’s also not nearly as broad as a amateur (ham) license.

Edit: I forgot that the Baofeng radios can also transmit on frequency ranges that are technically outside of the legal ham/GMRS allowed frequencies, like business communications, police/fire, etc. Be warned that even with a ham license there will be some things you aren’t legally allowed to do with this device. It’s definately not a toy.

Any pointers for learning the basics on this particular machine?

Again, it will depend on the model, but personally I find the Baofeng/Chinese model radios a giant PITA to use. They’re cheap, sure, but aside from using the programming cable they can be much more difficult to program/use as compared to the Japanese models like Yaesu or Icom.

I should read the manual cover to cover, right?

Sure, I suppose. :)

Looks like it’s easier to program from a computer, any tips on that?

I can highly recommend CHRIP as good programming software. It’s also open-source: https://chirp.danplanet.com/

What's the model?

Is it terribly hard to get a license in your country?

Here (New Zealand) the exam is multi choice and the questions are all online, and local clubs will run "ham crams" to teach you the material over a weekend, at the end you sit your test. I had enough EE/RF knowledge that I crammed the rest in an evening and then passed the test :)

Also here, you can't legally sell an "unrestricted two-way radio" like the UV-5R to anyone but a licensed ham, and you can't import them without a special license (which is stupidly easy to get, you just need to be a ham and ask for one). Not that this stops randoms selling them on FB marketplace as "police scanners."