Does the Catholic Church permit the faithful to pray the prayers appropriate to the chotki?
Yes.
Are the chotki prayers of Eastern Orthodox origin?
Doubtfully. To my knowledge, the chotki prayers were said by the eastern monks in ancient times before the Great Schism. They are still said by non-Roman Rite Catholics in full union with Rome.
Does the Church have anything to say about the chotki prayers?
In The Raccolta (1946 version), an official collection of prayers of the Roman Rite of the Catholic Church,
“Jesus Son of David have mercy on me.” is indulgenced with 500 days and a plenary indulgence (given the usual conditions) if it is said every day for a month.
Therefore, the Catholic Church highly recommends this short prayer to the Son of God (and by logical extension other variants of the Jesus Prayer).
Is it ok to pray the chotki instead of the holy rosary due to the difficulty I find meditating on the mysteries and saying the prayers?
The repetition of the Jesus prayer is a spiritually fruitful way to pray. However, there is a particular greatness to the rosary and it should not be given up too easily. Numerous saints have affirmed the excellence and privileged efficacy of the rosary. The Blessed Virgin Mary at both Fatima and Lourdes explicitly requested the rosary to be prayed. Moreover, at least twelve encyclicals and several other papal documents exist on the subject the holy rosary, exhorting the faithful directly and indirectly to pray it regularly, with Leo XIII affirming its miraculous origin.
Perhaps focusing on a word or very small part of a mystery while reciting the Hail Marys would help. Alternatively, you could simply announce the mystery at the beginning of the decade and focus on the words of the Hail Marys until meditating upon the mysteries becomes more natural.