Some offices are using their own forms that are not available on internet (for example, Bangkok is using the one with additional stamped fields) and some of offices don't accept downloaded ones. In that case, you have to fill out them at the office again anyway.
, as a rule, applicants have to go in person. It depends on the immigration office how long in advance they would accept cancellation application. Many allow you to do up to a few weeks earlier, but there are offices that accept cancellation application only on the last day.
, you may be able to apply for visas at the Thai embassy outside Thailand. But you cannot apply for long-term extensions until you cancel the previous extensions and you also might be fined for not cancellation correctly, when you finally cancel the old one, up to 20K baht.
, That varies by embassy. Some require you to provide proof of accommodations for the whole period of your itinerary. Some accept for a few days or a week. Did you check the website of the exact Thai embassy/consulate you are applying for your visa?
, The easiest is completing the application after your visa is approved. You also may be able to use the reference number of your submitted application on the eVisa system.
Q1. can she get a re-entry permit within the validity of the initial stay? If yes can she then still extend the duration of her stay by 30 additional days?
-> Yes and yes. Or, as she is an Italian passport holder, she also can enter Thailand on the visa-exempt scheme with an onward travel ticket for 30 days (as standard) for free.
Q2. do we need to cancel it before she leaves or just leave and let it expire (she is 16 years old).
-> As a rule, a Non-Immigrant based extension has to be cancelled.
IF she is sure would never come back to Thailand on any long-term basis (only as a short time tourist), she can let it expire and wouldn't have an issue.