Is it necessary that every enlightened being is an all-knowing person? Are there any grades of enlightments according to scriptures?
I am answering acc. to Sri Vainava (VisishtAdvaita) Sampradayam
The Vedas exclaim that having created the vast universe, the Supreme Brahman holds it with perfect precision, pervading each and every aspect of it in its entirety. This truth may be accepted at an intellectual level by many of us, but to experience it as the absolute truth is the essence of Brahma Jnana or enlightenment
This Brahma Jnana is possible in two ways - Enlightenment from practice of Bhakti Yoga and Enlightenment via attainment of Brahmānandam (or Moksha).
What is Brahmānandam?
It is Permanent Realisation (Moksha) exemplified by equality of experience (Sayujya) in eternal, indescribably perfect fusion of seshAtva and Paratantriya to DivyaThampathiyAr (i.e., Divine Couple, namely, Sri Maha Lakshmi and Vishnu). jivAtmas that are given Moksha by srimannArAyaNa attain to excellence in Paramapadam (or Vaikuntam) and are blessed with this state of cognisance.
Enlightenment via Bhakti Yoga
It is possible as a consequence of the practice of Bhakti Yoga to attain Brahma Jnana. Azhwars, in their verses, describe their experiences of Brahma Jnana to the extent that language can facilitate it.
Having given the two grades of enlightenment, what remains is:
Is it necessary that every enlightened being is an all-knowing person?
No. It is possible to attain Brahma Jnana without attaining Siddhis such as Omniscience - Brahma Jnana attained through Bhakti Yoga can be of this kind.
Edit - Source: For definition of Enlightenment, I used the Hindu article. OP did not define the term himself, I chose to exercise this liberty. I believe this is the widely accepted definition. The body of the answer draws primarily from Naalayira Divya Prabandham
There is no evidence that one becomes omniscient - Ramakrishna Paramahamsa, Ramana Maharishi being some examples - although they are able to read minds.
Question : What are kevala nirvikalpa samadhi and sahaja nirvikalpa samadhi?
Ramana Maharshi : The immersion of the mind in the Self, but without its destruction, is kevala nirvikalpa samadhi. In this state one is not free from vasanas and so one does not therefore attain mukti. Only after the vasanas have been destroyed can one attain liberation.
Question : When can one practise sahaja samadhi?
Ramana Maharshi : Even from the beginning. Even though one practises kevala nirvikalpa samadhi for years together, if one has not rooted out the vasanas one will not attain liberation.
Question : May I have a clear idea of the difference between savikalpa and nirvikalpa?
Ramana Maharshi : Holding on to the supreme state is samadhi. When it is with effort due to mental disturbances, it is savikalpa. When these disturbances are absent, it is nirvikalpa. Remaining permanently in the primal state without effort is sahaja.
Question : Is nirvikalpa samadhi absolutely necessary before the attainment of sahaja?
Ramana Maharshi : Abiding permanently in any of these samadhis, either savikalpa or nirvikatpa, is sahaja [the natural state]. What is body-consciousness? It is the insentient body plus consciousness. Both of these must lie in another consciousness which is absolute and unaffected and which remains as it always is, with or without the body-consciousness.
What does it then matter whether the body-consciousness is lost or retained, provided one is holding on to that pure consciousness? Total absence of body-consciousness has the advantage of making the samadhi more intense, although it makes no difference to the knowledge of the supreme.