I tried to simplify some of the sentences, as you suggested to me. Can you please check if everything is OK?

1) Puritans was the name given to the more extreme Protestants within the Church of England. They disapproved of both the rites and the bishops of the Church of England and wanted to reform the doctrines and the structure of the church. In particular, they wanted to purify the church from any trace of Catholic influence.
2) Charles I, however, believed he was king by divine right and refused to give up command of the arm forces. For this reason, Civil War broke out.
3) The forces were divided into the Royalists and the supporters of Parliament, led by Oliver Cromwell. The former had long hair and were known as “Cavaliers”. They included the lords, the gentry and the Church of England.
4) The latter were called Roundheads because they considered long hair sinful and wore their hair short. London, the ports, the Navy, the new gentry, small landowners, artisans and puritans sided with Parliament.
5) After the King’s execution on January 39, 1649, monarchy was abolished and the reign was ruled as a republic known as Commonwealth.

1) The name Puritans was given to the more extreme Protestants ...

2) Charles I, however, believed he was king by divine right and refused to give up command of the armed forces. For this reason, Civil War broke out.

3) The forces were divided into the Royalists and the supporters of Parliament, led by Oliver Cromwell. The former had long hair and were known as “Cavaliers”. They included the lords, the gentry, and the Church of England.

4) The latter were called Roundheads because they considered long hair sinful and wore their hair short. London, the ports, the Navy, the new gentry, small landowners, artisans, and Puritans sided with Parliament.

5) After the King’s execution on January 39, 1649, monarchy was abolished and the reign was ruled as a republic known as the Commonwealth.

1) The Puritans were a group of Protestants within the Church of England who were considered more extreme. They disagreed with the practices and authority of the Church of England and wanted to reform its beliefs and structure. Their main goal was to rid the church of any influence from Catholicism.

To simplify the sentence, you could say:

"Puritans were extreme Protestants within the Church of England who wanted to reform the church, particularly by removing any Catholic influence."

2) Charles I, on the other hand, believed that he was the king because of divine right and refused to give up control of the armed forces. This refusal ultimately led to the outbreak of the Civil War.

To simplify the sentence, you could say:

"Charles I believed he had the right to rule as king by divine right and refused to relinquish command of the military, which led to the start of the Civil War."

3) The opposing forces during the Civil War were divided into two groups: the Royalists and the supporters of Parliament, led by Oliver Cromwell. The Royalists, also known as "Cavaliers," had long hair and included members of the nobility, landed gentry, and the Church of England.

To simplify the sentence, you could say:

"The Royalists, commonly referred to as Cavaliers, had long hair and consisted of nobles, landed gentry, and members of the Church of England."

4) The supporters of Parliament, known as "Roundheads," earned their nickname because they believed long hair was sinful and therefore wore their hair short. In the conflict, the city of London, as well as ports, the Navy, newly wealthy individuals, small landowners, artisans, and Puritans, sided with Parliament.

To simplify the sentence, you could say:

"The Roundheads, who opposed long hair due to religious beliefs, consisted of the city of London, ports, the Navy, newly wealthy individuals, small landowners, artisans, and Puritans who aligned with Parliament."

5) Following the execution of the king on January 30, 1649, the monarchy was abolished, and the country was ruled as a republic known as the Commonwealth.

To simplify the sentence, you could say:

"The king was executed on January 30, 1649, leading to the abolition of the monarchy and the establishment of a republic called the Commonwealth."