As a Brazilian, I think the US banks are very strange.
"Swipe" cards have been phased out years ago - you'd have to try hard to find a bank which will still issue one.
Specifically because you can no longer find ATMs which rely solely on the magstripe. Some banks have biometric fingerprint readers (where you put in your hand and it reads multiple fingerprints at the same time) in addition to the PIN code of the debit/credit card, and sometimes additional passwords.
My bank does not rely on biometrics, but in order to do any transactions, I have to enter a code generated by the bank which consists of three strings, which are prompted one at a time, displayed on screen mixed with other random and unrelated strings, so that someone peeking over my shoulder would not be able to match the button with what's on screen and finally, before the transaction is complete, the account's password. And that's with a chip.
The portable readers you can find everywhere still have magstripe readers in addition to the chip reader and will refuse to read the magnetic strip if the card contains a chip.
Those portable readers use either a 3g connection or standard dialup.
As for the physical "imprints", this is something that 30-somethings like me can barely remember.
Also related: there are no bills which can't be paid online. All banks accept them, unless specified otherwise (usually there are restriction after the expiry date). If you get a bill by mail (instead of email), you can just type the barcode. Or scan it, if you have a reader or a mobile phone with the bank's app.
The concept of getting bills by mail, and then mailing back cheques, as found in the US, is completely alien.