Gmail on Android separate from google play Is there any way to read mail (and calendar) from a gmail account on a Android phone without tying the account to a play-store account used on the same phone? 
Theoretically this should not be a problem, gmail offers pop3 and IMAP so i should be able to use a client app and keep google ignorant of the device i use.

I ask because so far i have not connected my gmail account to my bank account or credit card and i would like for these to stay disconnected. 
Bank and credit card account identify me by name and surname (phone, address) while gmail is tied to some of my web activities (for example search history). I dont want to make it too easy for google and all those foreign governments to connect the two.

Here are some related questions:
How do I remove all social integration features with Google+/Google applications
and 
What information does stock Android send to Google by default, and how do I opt-out?. I would like to set up my new Android phone one step at the time, starting with the gmail and playstore account.
Yes, you can set up multiple Google Accounts on your device and Gmail will handle them with aplomb.

You may have to have the Play Store account be the "main" account, just for ease of use, but you can easily add the account(s) where you have your email and/or calendar information. You can also selectively choose which account syncs Gmail, Calendar, etc.