delta lake itself is free. It is a file format. But you will have to pay for storage and compute of course.
If you want to use Databricks with delta lake, it will not be free unless you use the community edition.
Depending on what you are planning to do, the cost can be very low to very high.
You can use delta lake without databricks btw.
About your 2nd question: pandas is indeed an option. And your concern is exactly why distributed data processing frameworks like Spark were created.
If you want to avoid using Spark, you might wanna look into Dask or Ray.