Go to Wikipedia - there is a lengthy write-up there.

The answer depends on the type of ticket. If you are asking about general admission entry tickets - you don't reserve those free kid's tickets in advance. Instead you collect them on the day of visit at one of the designated pick up points. Be sure to bring the kid's passport to the Colosseum for proof of age - some employees will ask for proof.

It is usually left up to the discretion of the employee at the security check. Typically small umbrellas are allowed inside while larger umbrellas are sometimes not. If you are worried about the sun, you might also want to consider one of the night tours of the Colosseum that are currently offered five nights a week.

Yes, you can enter the Roman Forum and Palatine Hill before visiting the Colosseum although it must be within the validity period of the ticket. Tickets are valid for either 24 or 48 hours depending on ticket type.

I would recommend against an Omnia pass - you will lose money if you make such a purchase. There is lots of information on the Rome Tripadvisor forums which explain why you don't want to make such a purchase. But if you like throwing away your money and decide to purchase this pass, you will still need to make a timed reservation to the Colosseum. You don't have to purchase tickets, but you do have to go to the official ticketing website and reserve your entry time.

Wow - you are reading websites / blogs with lots of incorrect information. First of all, more tickets will be released on the official website for your visit dates - so why don't you just wait for the next ticket release on CoopCulture and buy then? The next ticket release for those dates will be 7 days in advance of visit. So more tickets for July 25 are being released today, more July 26 tickets will be released tomorrow, and so on. Earlier this year, no one could buy tickets at the on site ticket office - not because they were sold out, but because the ticket office was closed due to COVID-19. However, the ticket office was re-opened in mid-May and it would be an alternate way of purchasing tickets if you decide to not buy online via one of the future ticket releases.

Anyone under the age of 18 qualifies for a free entry ticket. Be sure to bring their passports to the Colosseum for proof of age. Some employees will ask to see their passports to verify that they qualify. If you opt for a tour, there is a different age limit for free tours (under 5 years old) - so in your case, you would choose the option of the free entry ticket with a paid tour.

The earliest you can book a ticket or tour on the official ticketing website is 30 days in advance. Therefore, whatever website you used to book August 26 tickets was not the official website - you booked via a third party. And I am not surprised that you received a cancellation from a third party for an Underground tour - that happens frequently and would be a risk through any of the third party sellers including Tiqets

You can get the tickets through some local travel agencies

It is up to you. There are plenty of non-Italian speaking visitors who book the Italian language tour. Even if you don't speak the language, I think it is a bad idea to listen to an audioguide in another language during the tour. There could be a safety issue that the tour guide is trying to alert you about - and if you have an audioguide on, you may just completely ignore the warning - maybe putting you or someone else in danger. Also remember that night tours are different than daytime tours - the night tour is completely escorted with no time to visit on your own. The night tours also do not include a visit to the Roman Forum + Palatine Hill - you will need to purchase a separate ticket if you wish to visit the Roman Forum + Palatine Hill.