HSA Questions

I was discussing HSAs with my manager yesterday because we were trying to sort out all of the various benefits our company gives regarding medical reimbursements.

The HSA account offered by our health insurance comes with a $3 monthly maintenance fee. My employer agreed to pay the fee for everyone who opted for the HDHP+HSA. But, I know that the annual contribution limit for your HSA is the amount of your deductible, $1100 in my case, and in order to reach that max I’m having money taken from my paycheck each month. My employer than sends that money along with an additional $3 to the bank. Does anyone know if that additional $3 a month will go against me for that limit? Will I still end up with $36 less in my account at the end of the year?

I’ve read that I can open an HSA at any bank, as long as I can prove my enrollment in an HDHP. Does anybody know where I can find a no-monthly-fee bank for my HSA?