Student or Learner
The word is, "intelligent".
The sentence is, "She is intelligent."
1. Is a comma needed after "is" in the sentences?
2. Is the full stop in the correct place in the sentences?
I think the comma makes the meaning clearer, as it reflects the speed and intonation we would use to make it clear. But strictly speaking, it is not absolutely necessary in my view (I am against hard-and-fast comma 'rules.')
The full stop is correct for Brits, but Americans would likely place the period inside the quotes even in the first example.