2.Planning to visit Colosseum, Forum & Pantheon in evening around 3pm? - What tickets needs to purchased from http://www.coopculture.it/en/ticket_office.cfm Should I go for
underground tour ?
Nanban, you need to purchase two (assuming you're traveling with a spouse) adult tickets for 14,00 € apiece (COLOSSEUM-ROMAN FORUM/PALATINE > FULL PRICE+RESERVATION) and two 'free' tickets for the kids at 2,00 € apiece (COLOSSEUM-ROMAN FORUM/PALATINE > FREE+RESERVATION ). The 2,00 € is a reservation fee.
The Underground/Third Ring tour would be separate, additional purchase. The three sites (Colosseum/Forum/Palatine) together take a bit of time to do so I think adding the underground/ring tour might be overkill for the kids.
I don't have any personal experience with this company but they're seeing very good reviews for their tours designed specifically for kids:
https://rometourswithkids.com/colosseumtourwithkids.html
A thought, maybe? The forum, especially, is a really confusing site without a good guidebook, and that's the one I'd be concerned about as far as a boredom factor. They do not 'do' the Palatine but as the tour ends in the Forum, you could always walk through that when your guide takes his/her leave: I'd inform them if that's what you wish to do so they can point you to the best way to access it.
Other RS member may have firsthand experience with kid-focused tours that they could recommend as well.