Good day fellow travellers. Someone suggested to me not to reserve my train from Rome to Florence in advance, as it is more expensive. Is this true? Same with Uffizi/Academie museum reservations? Thanks

I am not sure about train reservations, but I didn't think there was a charge for the reservation. That said, depending when you are traveling it is quite likely you won't really need to reserve them much in advance.
As to the Uffizi and Academia, if you call 39-055-294-883 you can connect with an English speaking operator that will make your reservations for either/both museums. There is a charge of a couple euro for the reservation, the "secret" is that you don't pay for the reservation until you pick it up, so if you get to the museum and there is no line, you just go through the regular entrance and don't pay for the reservation. If you get there and there is a line, you go pick up the reservation and pay the extra couple euro.
Stan

If you book your Rome-Florence ticket in advance at raileurope.com, you will pay an inflated price. Unless trenitalia.com is offering an online discount, the price there and the walk-up price will be the same. However, for Rome-Florence there really is no need to book from home. Assuming you'll be in Rome a few days before going to Florence, just buy your ticket a day or two before you're ready to make that trip.
There is no need to book ahead for the Rome-Florence train. There is a frequent service between the cities and even if the first train is full you'll get on the next an hour or so later. We just turned up and bought our tickets for the next train in both directions a couple of years ago - a Sunday lunchtime and a Friday morning.