I really need you to check these sentences. Thank you.

1) Shakespeare meditates whether time is preordained or not inevitable, the result of human activity.
2) The concept of the universe as a cosmic dance was derived (induced) from the new scientific discoveries, which described the universe as (being) in perpetual movement.
3) In the night (on the night?) of the murder the earth trembles.
She tells him to put his nightgown on /to put on his nightgown. (both correct: where can I find the grammatical explanation?)
4) The most dominant themes in Shakespeare's plays are those of the regicide, the reversal of values, the false appearances and time. (How can I best introduce all the themes at the beginning of a paragraph?).
5) Example: Various themes are present in Shakespeare's Macbeth. First, that of regicide, that brings about chaos and terrible weather conditions. Second, ...
6) She gives advice/suggestions to her husband on how to behave. (She suffests how he should behave??)

1. Shakespeare meditates on whether...

Delete "not inevitable" - it's redundant.

2. ... a cosmic dance came from the new...

3. On the night...

"to put on" = a phrasal verb -- http://grammar.ccc.commnet.edu/grammar/verbs.htm#phrasal and http://www.englishclub.com/grammar/verbs-phrasal-verbs.htm

4. delete "the" before "regicide" and before "false"
comma after "appearances"
The way you have phrased this is just fine. Check out the 5th example here:
http://leo.stcloudstate.edu/acadwrite/thesistatement.html
Your sentence is like that one.

5. #4 is better.

6. suggests -- yes, all are fine.