Is it mandatory to pay an annual credit card fee?

You may have to pay an annual when you're first taking out a credit card. However, after some time, if you use your cards for a substantial amount, you can request to waive of the fee.
if your annual fee is still not waived off, you can shop for a suitable card from other creditors. Usually, there are some T&C that you need to qualify to take out a card without any annual fee.

Usually, you have to pay an annual fee for credit cards. But there are many ways to waive it off. Some credit card companies waive annual fees in the first year. After the first year is over, you can close the account to avoid the annual fee.

Yes, you should pay the annual fee for keeping a credit card. Sometimes, the credit card company waive it off based on how well you manage your credit card. Try to be regular on your credit card bill payments.

Sometimes, you may take out a credit card with an annual fee but it gets waived off when you swipe your card for a certain amount. However, while going for such a card, make sure that you'll be repay the amount you're swiping. Don't get enticed to shop more that you can't handle financially.
However, as others have said, you can shop for a card without an annual fee. But, a card with a nominal fee can give your better cashback offers or rewards annually.