Yes. Password protected wifi - even if everyone knows the password - is more secure, as the data between your device and the router is still encrypted.

I think you're misinformed.

While the *authentication process* is encrypted (negotiating the WPA password, etc), that does not make all your data encrypted after the connection. That's the importance of using HTTPS vs HTTP protocols for websites/apps.

Once you're connected via the shared password, the wifi is no more or less secure than an open wifi network, except you're keeping away from random devices/people who don't know the pre-shared key.

Subsequently, even on open wifi, if you're using HTTPS to connect to your bank, every single packet sent to your bank is not sent unencrypted.

I'm worried you're under the impression that connecting via WPA to a WAP means all your data is encrypted between the client and the WAP, and that's.... not at all how it works.