To start sharing a file tap on "+" -> Share file, select either Photos app or browse for other apps. Multi selection is not possible though this flow, and files are to be sent one-by-one.

To receive a file from remote peers tap on "+" -> Scan QR code and scan the shared QR code.
If you go to "Downloads" folder and tap on "link" icon at the upper right corner, you'll see history of all file download transfers. Tap on each to see details about each transfer.
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