Sentry and other application profilers for Python are used to improve Django services' performance by capturing every single function call taking place in a given operation. Code optimization is essential for improving the quality of code and efficiency, and it involves writing code that takes the least time to execute. The Django Debug Toolbar provides insights into performance monitoring data, while profiling tools like cProfile and django-silk make it easier to analyze slow parts of the code. Persistent database connections can be maintained by using connection poolers or adding `CONN_MAX_AGE` in settings.py. Scheduling tasks is crucial for processes that take a long time to execute, such as sending emails via external providers, and tools like celery can help with this. Third-party dependencies can add unnecessary overhead on code and cause applications to run slow; it's essential to ensure these packages are up-to-date and not too many are used. Loops can be replaced with map() functions where needed to save memory and improve performance. Using the latest Python version, NumPy, and Sentry can also significantly enhance Django project performance.