Parallels Desktop is not a simple offline program. It is deeply integrated with online servers. When you purchase a license, you are issued a unique activation key. When you enter this key, the software communicates with Parallels' servers to verify its authenticity.
While a permanent full version is a paid product, you can use it for free through official channels: Parallels Desktop Activation Key- Free
Yes, via the 14-day trial. After that, you must pay. For a free long-term option on Apple Silicon, use UTM. Parallels Desktop is not a simple offline program