alana,
There are two primary routes from Vernazza to Venice, one through Milan and one through Florence. I've found that the Florence route is often a bit quicker. As a previous post mentioned, the schedules for the latter part of the year won't be uploaded until mid-June, so that's why you're not able to find any solutions for 7 Sept. I'd suggest choosing a date in the next week or so on the same day-of-the-week that you'll be travelling, and that will provide a "ballpark estimate".
A few thoughts on your questions.....
1.) I didn't check cost but for best time, I'd use a departure at 09:28, arriving Venezia S. Lucia at 14:20 (time 4H:52M, 3 changes at La Spezia Centrale, Pisa Centrale & Firenze SMN, reservations compulsory on second and last segments). The first and third segments will be Regionale so DON'T forget to validate your tickets prior to boarding the train on the day of travel. That route is consderably quicker than most of the others.
2.) Venice to Rome is very easy as there are departures about every hour and most of the trains are direct, with a travel time of 3H:45M via Freccia high speed. You can take your pick of departure times. It's not likely that the new schedules will change much from the present ones. Second class Base fare (the highest price tier) is €80 on that route. I wasn't able to see Economy and Super Economy as they appear to be sold out for this month. Super Economy typically ranges from €9 - 39 and Economy ~€49. You can purchase tickets up to 120 days in advance but be sure you're willing to commit to a specific train, date and departure time, as the tickets will be valid on only ONE train. If you manage to get Super Economy tickets, they're non-changeable and non-refundable, so choose carefully! Note that your departure station will be Venezia S. Lucia and arrival station Roma Termini.
3.) I'd suggest waiting until 120 days from your trips before trying to book on Trenitalia. You'll be able to easily buy tickets for the "fast" trains such as Freccia or InterCity, but purchasing Regionale tickets is awkward and they're more restrictive if purchased online. Best to buy those when you arrive in Italy, either from a Kiosk or a staffed ticket office. The Trenitalia website will show all classes of tickets that are available in the "Offers" column.
One other point to mention is that you can also use the competing Italo high speed trains from Venice to Rome, although they often arrive at Roma Tiburtina rather than Roma Termini. Have a look at their schedules to see if that might work for you.