Jeanie,
I was in the same boat as you. I had the Fidelity Visa and Amex and wanted to open the Cash Management account. As far as I know, there were no pulls for that account. Note that it's technically considered a brokerage account, not a checking, savings, or credit card account.
I use the Fidelity Cash account as my primary checking account for check deposits via the mobile app, and ATM withdrawals. Fidelity reimburses ATM fees next day, and I've never had an issue. I deposit checks all the time and have never had an issue. Take a picture of the front, take a picture of the back, and store the check until it clears (just in case).
As a primary checking account, I like it for the reasons above other than the ability to deposit cash/checks in person. I have another bank nearby that I deposit cash to, and then use the online interface to transfer between accounts. I don't use my Fidelity account for bill pay or checkwriting (Bluebird / credit card auto-pay), so can't help with that.
I'm not sure who issues the debit/ATM card, but it does not have a chip. Can't speak to foreign transaction fees either, as I use it purely for the reasons above.
Hope this helps.