If I don't have a credit card, can I still download free apps?

Here’s how to remove all payment methods:

Change, add, or remove Apple ID payment methods - Apple Support

If you can't remove your last payment method or use no payment method with your Apple ID - Apple Support

Also, Apple Gift Cards can be used to purchase apps, if you need or want non-free apps.

https://www.apple.com/shop/gift-cards

In addition to all the advice above, be advised that most "free" apps have "in-app purchases." Without a valid payment method on your account, you won't be able to download any free app with in-app purchases. This will greatly limit the number of free apps you can actually download.

Change, add, or remove Apple ID payment methods - Apple Support