Is it normal that running python under valgrind shows many errors with memory?

You could try using the suppression file that comes with the python source

Reading the Python Valgrind README is a good idea too!

Following links given by Nick I was able to find some updates on README.valgrind. In one word, for Python > 3.6, you can set PYTHONMALLOC=malloc environment variable to effectively disable the warnings. For example, in my machine:

export PYTHONMALLOC=malloc
valgrind python my_script.py

doesn't produce any error related to python.