You're right that you can't download multiple files on the phone. (Whether that's a good decision or not I don't know -- generally whenever I try sharing multiple files in iOS apps it's wonky, where apps only receive the first file and throw away the rest, so it might be a broader ecosystem problem.)

But just use your browser. Ctrl+A to select all files, hit the "Download" button, wait a minute for it to create a .zip file, and it downloads. Just tried it myself, works like a charm. (In past experience sometimes the .zip archive step fails -- if so, so just try a second time.)

> I also can’t make an actual copy of the files without downloading and uploading so they save some precious space.

If you're trying to make a copy to your own personal Drive, just select "Make a copy" from the context menu. That creates a copy (not a shortcut) in your Drive root folder, no downloading and uploading required. (In the mobile app that option appears only for individual files, but the Drive website allows you to do it for all selected files at once.) I just tried this now as well and it works perfectly.

Or if you want to save space on your Drive, you can drag them to "My Drive" (rather than explicitly making a copy) and it'll create shortcuts instead.