Can I get Mac Java Edition for free after buying Windows Java Edition?

Since Java edition is linked to your Minecraft account, and there are multiple versions on the site for download, yes. You can get Java edition for free (as long as you log into the Minecraft account that purchased it).

But if the same account is in-play, it will either:

• log the current player out, or
• deny you access.

Minecraft Java Edition covers all platforms that Java runs on, so... Yes.

Including Linux.

Minecraft Java Edition works on Windows, Mac, and Linux. You can install Java Edition again for free only if you use the same account as the one you used to install Java Edition for Windows.