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All things being configured correctly and all parties playing by the rules ..
The outgoing edge of the public 'free' VPN server will see all data as it is presented to the internet. The VPN layer of data encryption is between you and the public VPN server not the subsequent HTTP/S website.
Theoilman wroteIn other words is it safe to use openvpn with a public server for sensitive data on sites with https?
The 'free' VPN server will see data encrypted at the HTTPS layer as encrypted, the VPN server cannot decrypt the HTTPS layer. ***
See my first condition ..