1) Most cruise stops are like, 8:00 a.m. Til 5:00 p.m. Though some are longer. Often, there will be one or more overnight stays in port. On a recent transatlantic, we overnighted in NYC, enabling us to take in a Broadway show.
2) No. You can't depart the ship until port authorities clear it, and it takes some time to secure it to the dock & get the gangways. In place.
3)This is something that goes into selecting the cruise. The Mega-Ships consider themselves a floating resort- why would you want to leave it? But many smaller vessels stop at smaller, very interesting ports and allow time for exploratoin. Some ports are more convenient than others The port for Rome, Civitavechia is over an hour by train from the city. Same for the ports for Paris & Berlin and others. Choose your cruise carefully. Also plan how to get back to the ship before it departs. You don't want to be standing on the dock as it sails over the horizon. You're on your own to get to the next port and rejoin it.
4) There is no set price. But if I'm pulling a number out of thin air, I'd say around $100 pp. More complex excursions cost more, simpler ones, much less. If there is a seaplane flight to go salmon fishing in Alaska will cost more than a walking tour or half day city bus tour. You can book the same excursions as the cruise line and cut out the middle man. When you book a cruise, go to
www.cruisecritic.com (this is important) and join your cruises' 'Roll Call.' There is one for virtually every cruise unless it's tiny. There you will 'meet' other people who will be joining you on your cruise. Many of these will be experienced, and will be booking private excursions at your port stops. As well as parties aboard, or to find dinner companions.
Jim