A: No. The two products use separate licensing systems; you need to buy two licenses if you would like to use both products.
Q: Are the project files compatible between IntelliJ IDEA and PyCharm?
A: Projects created in PyCharm can be opened in IntelliJ IDEA with Python plugin installed without any issues. IntelliJ IDEA allows a more flexible project configuration, such as the possibility to configure libraries for projects. PyCharm will be able to open and work with projects that use the more advanced settings, but you will not be able to change the settings in PyCharm.