Also, does this ticket cover the general entrance into the Colosseum
as well?
No, you have to purchase an additional entry ticket. It's noted on the page where you go to reserve your tour in English:
"IN ORDER TO VISIT THE UNDERGROUND IT'S ALSO NECESSARY TO BUY THE COLOSSEUM ENTRANCE TICKET AT THE RESERVATION DESK"
That desk is where you go to check in for your tour. Children under 12 are free for the tour but must have a reservation (the 2 euro "free" reservation) and those over 12 pay the same price as an adult. Your children under age 18 will not need to have an additional entry ticket but proof of age is required at the check-in desk, as well as proof of age for the under-12 tour reservation.
It's possible to pre-purchase your separate, adult-entry tickets online but just as easy to get them at the desk.
There is a very thorough explanation about how all this works on Trip Advisor (written by an RS member, I believe) if that helps?
https://www.tripadvisor.com/ShowTopic-g187791-i22-k8145551-How_to_book_the_colosseum_underground_tour-Rome_Lazio.html