The Maronites are Catholic; there is no corresponding Orthodox equivalent.
The Melkites are Catholic; their orthodox counterpart is the Antiochian Orthodox Church.
Both are fully in union with Rome. The Maronites were out of communication but never in scism, for several hundred years, coming back into communication and reaffirming their unity in the 12th C. The Melkites had been the Antiochian Orthodox; the majority of the synod voted to come back into union, and did so; The modern AO are the synodal minority from that decision; they left the synod to remain free of Rome.
Both are also Patriarchal Churches; They consider their union to be one of equals, not one of submission, per se. The head of their church is their Patriarch, who is in Union with the See of Peter, and the visible head of the Catholic Union of Churches, the Pope.
They are fully valid and fully licit; you can fulfill your sunday obligation with them, and can receive all the sacraments (except ordination) as a Latin.
The Eastern Catholic churches have a separate body of Canon Law from the Latin Church; some things done in Eastern Churches are forbidden to be done in the Roman Church. EG: Using leavened bread for the Eucharist, churches without confessionals, no holy water at the doors, married priests.
Is holy water not used at all? Why? I have never even thought about why we have it… Priests can marry after ordination, or they had to be previously married? [like our Deacons] Are the beards required for men? I notice all Eastern priests I have ever seen [in photos, I have never seen one personally] have beards.
Ordination is reserved to persons of the same Rite as the church they are ordained to serve in, with a strong preference that they be of the same church sui iuris.