I'm posting you the sentences I'm most dubtful about. I included my doubts in parentheses.

1) Despite his victorious military campaigns Cromwell introduced unpopular restrictions on everyday life, such as, for example, the closing (?) of the theatres for their supposed immorality in 1642.
2) Copernicus’s scientific discoveries were then supported by Galileo Galilei and Johannes Kepler, who contributed to putting forward a new model of the universe.
3) Like the new science, philosophy rejected the old deductive method in favour of the inductive method, according to which (?) general truths resulted from particular facts.
4) This meant that sense experience became more important in the (? is "the" necessary?) establishing the truth than traditionally accepted ideas.
5)A witch-hunt was organized (?) first in Denmark then in Scotland to find the witches, who had attempted James's and Anne's lives.

2 answers

1. comma needed
delete "for example" and two commas before "the closing"

2. Copernicus' (no need for the extra "s" on a multi-syllable word)

3. OK

4. sense = ??
No, "the" is not needed.

5. comma after "organized" and "Denmark"
I don't understand "had attempted ... lives"
5. comma after "Scotland" too