I am assuming the skip the line ticket is the same as time slot entry,
correct?
First, understand that there is no "skip the line" ticket. ANY ticket purchased in advance will allow you to skip the TICKET queue but not the security-check queue. Everyone has to go through that one. There are separate entry lines for people with timed tickets and people without. The important difference is that a general-entry ticket will only allow you to enter the Colosseum after 2:00 PM. If you MUST visit the colosseum before the afternoon, then buy a timed-entry ticket online for any available open slots in the morning.
In any case, delays are possible with any ticket if the thing is filled to capacity: wait times can occur if some visitors have to leave before others can enter.
If you are just purchasing general-entry, non-timed tickets and don't want to do it online, then yes, you can do that at the Forum or Palatine entrances. These two attractions are CONNECTED and must be visited at the same time. Once you have your ticket, you can visit them in the morning before 2:00 entry to the Colosseum. I would advise getting to either of their ticket offices first thing in the morning before they open.
Roman Forum: Largo della Salara Vecchia 5/6
Palatine Hill: Via di San Gregorio 30
Yes, you are very likely much too late for underground tickets through the coopculture website. That's a wildly popular tour and tickets go very, very quickly. Whether buy a tour through an outside company is entirely up to you: it's personally not something I'd spend the $ on as you can see down into the exposed underground from above "general" areas.
But here's a suggestion? Take a look at this coopculture tour:
http://ecm.coopculture.it/index.php?option=com_snapp&view=event&id=E6A1B5B3-BFDA-AC94-6929-0161B2E3A0C0&catalogid=5FF3365D-8688-FC84-2265-01651507C590&lang=en
It doesn't do the underground but will provide narration of the structure's function for a very attractive price (€ 12,00 full entry ticket + tour € 5,00 + € 2,00 reservation). Looks like there are still English tours available for the 15th.
Book it online and choose the pickup@ticket office option if you can't print the tickets out in advance. If you go this route, you'll have to visit the Forum/Palatine AFTER your tour of the Colosseum. Give yourself plenty of time to your tour's meeting point, get through security and and pick up your tickets. If confused about where you're supposed to go, ask a guard.
