Since faba bean contains levodopa should it be taken by parkinson patients?

No evidence for this. Fava beans do have levodopa, but the amount in any individual bean is very variable and small. It likely won't hurt, but medications should be much more helpful and more reliable.
Faba bean. The bean does not have enough Levodopa content to treat parkinson. You will need to eat tons of beans to even see an effect.