Word – How secure are password-protected zip files

The compression offered by 7zip (in the 7z format) is more secure than any of the "standard" methods or encrypting a zip format file (many of which date back years and are barely secure at all). In either case make sure you chose a good password/key - with a badly chosen password all encryption techniques are susceptible to dictionary/guess attacks.

If you are encrypting files to send to someone else, GPG would be better (see https://help.ubuntu.com/community/GnuPrivacyGuardHowto for some Ubuntu specific notes, or Google for many other similar resources) if the person you are sending to is capable+willing to use GPG/PGP/compatible (or is already using them). The standard GPG tools are command line driven so easy to work into scripts if you are archiving files regularly and want to automate it. This is public key based so removes the problem of trying to get the key to the recipient by secure means as you encrypt with their public key and only they have the private key needed to unlock the resulting file (even you, the person who encrypted the file in the first place, would not be able to decrypt it). For paranoia++, encrypt with 7zip as you make the archive then with the recipient's public key via GPG.

No, Windows does not provide this feature.

Have you considered using a portable app? You can install the portable versions of WinRAR or 7Zip to your USB, and use them to zip and password protect any file/folder you want. That way, you don't need to install anything to your windows machine.