The Navy operated a very small number of B-17s (redesignated as PB-1s) as patrol and anti-submarine aircraft from 1945 - see Joe Baugher's PB-1 Naval Fortress page for further details. The main four-engine land-based aircraft of the Navy were derived from the B-24, the PB4Y-1 Liberator and PB4Y-2 Privateer.

Neither the B-17 or B-24 nor their naval versions could operate from an aircraft carrier; B-25 Mitchells were famously launched from the USS Hornet for the Doolittle Raid, but that was pretty much the limit; the B-17 was around ten metres wider and seven metres longer than a B-25, just fitting one on the flight deck would have been a challenge, let alone then taking off (or trying to land).

No, the B-17 was only operated by the Army Air Corps in the Pacific during the early parts of the war. The B-17 was not capable of being launched from an aircraft carrier.

Near the end of the war, the Navy did develop a B-17 variant designed as an airborne early warning (AEW) aircraft, which was designated as the PB-1W variant. I believe these aircraft arrived too late to participate in any operations in 1945, though. Here are some photographs of the PB-1W with the radar slung under the fuselage.

The Coast Guard also developed its own variant of the B-17 near the end of the war called the PB-1G designed for patrol/search and rescue operations. It carried a lifeboat that could be dropped by air; you can read a little about it here.

More common would have been naval versions of the B-24 Liberator, though these were also incapable of carrier operations. The PB4Y-1 was used extensively for anti-submarine patrols in the Atlantic, but also used for similar operations and reconnaissance in the Pacific. The PB4Y-2, nicknamed the "Privateer," was a modified version of the PB4Y-1 that arrived later in the war. It filled a similar role to its predecessor as a long-range patrol and reconnaissance aircraft.