Subjunctive: Is It Possible To Say "He Do" And Not "He Does"?

I have had trouble trying to figure out whether I can use "he do" in certain situation and not "he does" as the situation commonly requires it.

I'm so glad that I've found the solution to the problem. Thus, the sentence "he does this everyday" is correct but not "he do this everyday." However, "I insist that he do this everyday" is correct but not "I insist that he does this everyday."

Then there are also the problems of "I were, he were, she were". For instance, in the sentence "If I were the King of England", shouldn't it be written as "If I was the King of England"?

Bartleby.com says:

"According to traditional rules, you use the subjunctive to describe an occurrence that you have presupposed to be contrary to fact: if I were ten years younger, if America were still a British Colony.

"When the situation described by the if clause is not presupposed to be false, however, that clause must contain an indicative verb.

The form of verb in the main clause will depend on your intended meaning: If Hamlet was really written by Marlowe, as many have argued, then we have underestimated Marlowe’s genius. If Kevin was out all day, then it makes sense that he couldn’t answer the phone."

The key words here are "presupposed to be false". Simply put, if you have presupposed something to be false, use "were". If it's just a probability, use "was".

But, Bartleby.com says:

Remember, just because the modal verb would appears in the main clause, this doesn’t mean that the verb in the if clause must be in the subjunctive if the content of that clause is not presupposed to be false: If I was (not were) to accept their offer—which I’m still considering—I would have to start the new job on May 2. He would always call her from the office if he was (not were) going to be late for dinner.