But with the recent elimination of the free admission on the first
Sunday of the month...
They only eliminated the free first Sundays at State museums - state museums which are normally open on all Sundays anyway - during high-season months. For example, Included in the list of free days on the Uffizi website:
https://www.uffizi.it/en/pages/free-admission-days
"The first Sunday of the six months between October 2019 and March 2020: 6 October 2019; 3 November 2019; 1 December 2019; 5 January 2020; 2 February 2020; 1 March 2020."
For Florence museums, this will be helpful:
https://www.visitflorence.com/blog/free-museum-days-florences-top-museums-2019/
This is not true for the Colosseum in Rome. Free days for 2019 were announced early in the year and are as follows (excluding dates already past):
23rd of September
4th of October
4th of November
21th of November
18th of December
So you have to check each museum's website for their free-day listings
As far as I'm aware, the 2 € rate applies only to 18-25 year olds of EU citizens and those of non-EU mutual agreement countries. Again from the Uffizi site:
https://www.uffizi.it/en/pages/free-and-reduced-tickets
"REDUCED-PRICE TICKET ( 2 €+ reservation fee )
European Union citizens only, aged +18 | -26 upon showing passport or ID, and citizens of non-EU Countries only upon mutual agreement (Norway, Iceland, Switzerland, Liechtenstein)."
The same is true at the Accademia (see "reduced price"):
http://www.galleriaaccademiafirenze.beniculturali.it/galleria/1/visiting/
Reduced tickets (€ 6.00 including pre-sale + reservation fee) for Galleria Borghese are only available for citizens aged 18-25 of EU, Norway, Iceland, Liechtenstein and Switzerland showing valid proof. As this is an Italian State museum, it is free to visit on the first Sundays of October - March 2019/2020 but advance reservations are still mandatory.
https://www.tosc.it/tickets.html