Banking Facilities

Yes, HDFC charges some fees if you choose the auto sweep services. Additionally, HDFC charges fees for early withdrawals from fixed deposits. The threshold amount is entirely dependent on your spending and saving habits. Many set it at ₹25,000–₹50,000, hence just the additional money gets cleaned.

Regarding the hidden charges, it's advisable to consult with bank officials to gain further clarity on whether to choose this service or not.

NPS is a good option if you want tax benefits. However, if the lock-in period is your primary concern, there are alternative options available. ELSS mutual funds are a good option with only 3 years of lock-in period and also give you tax benefits under Section 80C. 
PPF is another tax-saving choice with a 15-year lock-in period, but you can withdraw a partial amount after 5 years. So managing NPS with these schemes gives you flexibility with both tax savings and less lock-in period.

HDFC, ICICI, and SBI Bank allow the opening of PPF accounts online. The current PPF interest rate is 7.1% which is the same for all the banks. Minimum Rs. 500 you need to deposit and it will go upto Rs.1.5 lakh annually.
Look for a bank known for good online service. Do some research online or visit banks' websites to compare features and choose the one that best suits your needs.