Do I have to buy an iPhone 12 Pro Max separately?

See the following from Buy iPhone 12 Pro and iPhone 12 Pro Max - Apple

As part of our efforts to reach our environmental goals, iPhone 12 Pro and iPhone 12 Pro Max do not include a power adapter or EarPods. Included in the box is a USB‑C to Lightning cable that supports fast charging and is compatible with USB‑C power adapters and computer ports.

We encourage you to re‑use your current USB‑A to Lightning cables, power adapters, and headphones which are compatible with these iPhone models. But if you need any new Apple power adapters or headphones, they are available for purchase.

If you need to buy a power adapter, see: Buy 20W USB-C Power Adapter - Apple

yes, you would need to purchase a usb c charger.

Note that you can also use your lightning cables from previous iPhones you may have owned.

20W USB-C Power Adapter

or Anker makes quite a selection as well, here is a directly comparable one

https://us.anker.com/collections/chargers/products/a2633