Is this the correct Hebrew spelling of the word timshel/timshol?

If you mean the word in Genesis 4:7, then yes, it is spelled correctly. But it doesn't mean what you think it does. תמשל = "thou mayest rule" with "rule," (or "lead," "control," or "govern") being the main meaning (from the root משל, meaning "ruler" or "leader.") The "thou mayest" is just a grammatical explanation added by the translator. For example, see Genesis 37:8, which is the other place this word is found in the Bible.