I'm not sure what the question is either but your itinerary looks fine. Some folks might say that 10 days is too long for Rome but I'll disagree: there is a LOT to see in that one, and you'll have the luxury of exploring it in more depth than most first-time tourists allow. You could even add another day trip to, say. Ovietto or Ostia Antica (both by train) if you wished to.
Florence offers a lot to see as well but is also a good base for day trips. Shave a day off Rome and you could add Siena (bus or train) or Lucca (train) in addition to your driving day in the countryside; both very popular choice amongst the gang here.
As you lose at least 1/2 a day every time you change locations, you'll realistically end up with 3.5 days for Venice. I would spend it all there with a boat trip or two to Burano and some other other islands.
Varenna is a good choice for the Lake Como area, and you could day-trip to Bergamo if you wanted to; only an hour or so away by train.
Yes, you absolutely do need to pre-purchase tickets for certain of the attractions in Rome and Florence. Have you made a list of what you want to see if both cities so we can point out which ones those are and how to do it?
As you've traveled in France, you're probably "up" on things like small hotels not having lifts and being able to manage your own bags on the trains and whatnot? The lighter, the better! Speaking of rail, if you're willing to commit to a specific time/train, you can land some nice bargain (non-changeable, non-refundable) rates by buying your tickets in advance.
There are some things you need to know about renting/driving a car in Italy but someone who can explain those much better than I ever could - we don't drive in The Boot - should be along shortly with those details. :O)
