Hello travel4fun,
We did the Secret Tour in September and it is essentially a guided tour of lowest dungeons, working up to the administrative offices, the upper cells and interrogation room, the Senate chambers and Casanova's cell and the intervening spaces. The descriptions of stairs and small spaces are accurate and I know in the Summer they only do morning tours because of the heat in the attic spaces. After the tour they take you to a point near the regular Dodge's Palace entrance and inject you back into the regular traffic flow.
The public spaces in the Dodge's Palace are mostly large rooms made to impress visitors and display the wealth of Venice but the Bridge of Sighs is included as a regular part of the Palace access now. I believe there are "more or less dungeon" options as you exit but beyond that it is essentially a one way flow. I think the Dodge's Palace is one of those places that context and information from a guide or a tour really helps add context and give some richness to what is otherwise just a series and rooms with impressive artwork. The understanding of the power, wealth and somewhat crazy nature of Venice's history add a lot of flavor to the story of Venice. The SI tour adds some of that context but is specific to what it covers.
I would count on spending between 1-2 hours there and add some time if you are taking the secret tour.
When you buy the St. Mark’s ticket get the addition for the museum part of the church. The museum is interesting by itself but the ticket also buys you access to upper parts for better views of the church itself and access to the roof to look out over Venice and the square. I think the Pala d'Oro is worth skipping unless you're really into altars. You can buy tickets for all the "upgrade" parts in the church itself as well if you want.
If you do Dodge's Palace in the morning and want get lunch check out Rossopomodoro a few blocks away. It's a Milan based Itallian fast food chain. They have take away but also a huge (for Venice) restaurant and American speed service which can be difficult to find for a quick lunch. It will not be your most memorable dining experience in Italy but it's decent food and it's fast if you have sights to see.
Enjoy Venice - it's amazing,
=Tod