Feather writes to the following paths:

What Linux macOS Windows
Wallet files ~/Monero/wallets/ ~/Monero/wallets/ C:/Users/<USER>/Documents/Monero/wallets/
Program data ~/.config/feather/ ~/Library/Preferences/ C:/Users/<USER>/AppData/Local/FeatherWallet/

Note: The wallet files location is configurable, see Wallet files for more information.

The Program data folder contains the following files:

What File Description
Configuration settings.json JSON file containing wallet settings
Tor program file ./tor/* Bundled Tor program files, placed here when Feather starts
Fiat history database fiatHistory.db Text file with on each row: YYYYMMDD:<XMR price in USD>
Log files libwallet.log* Monero core wallet implementation logs. Log files are not written by default.