Make a TAR or TAR.GZ

TAR.GZ, almost always — plain TAR does not compress at all, so the archive is the size of everything in it added together. Plain TAR is useful when the contents are already compressed, or when something downstream expects to do the compressing.

Yes, and that is tested rather than assumed: every build checks that GNU tar itself lists and extracts what this page produces, byte for byte. Long file names are written as POSIX pax headers, which is the standard extension and what bsdtar and 7-Zip on Windows read without complaint.

No. The archive is built on your own device and saved straight to your downloads. Your files are never uploaded, which is the point: the things people most often need to zip — documents, photographs, a folder of work — are exactly the things that should not be handed to a stranger's server first.

Mostly because something else asked for it — a server, a deployment script, a colleague on Linux. There is one real technical advantage: because TAR.GZ compresses the bundle as a single stream rather than each file separately, it is often noticeably smaller than a ZIP when you have many small similar files, like source code or logs. For sending one archive to one person on Windows, ZIP is the friendlier choice.

Your device's memory rather than a server's upload cap. Hundreds of files and several gigabytes are fine on a normal computer; a phone will manage less.