"I demanded him to apologise" doesn't sound right. If you change the verb to "ask", it would be fine.
As for the second set of sentences, the first one is commonly used because most native speakers have no clue about the use of the subjunctive, but the second one is technically correct. Both would be understood and only picky grammarians would take issue with using "is" instead of "be". If you're taking a formal English test, go with the second sentence.