Thanks for the great help in providing answers to our well versed civilian questioner.  The following is a compilation of the answers that we all put together (with special thanks to Jim Christley and Donald Johnson)

While the Thresher/Permit Class is similar in size and shape to the Sturgeon Class, there are major differences in hull and Fairwater shape, equipment installed, and other capabilities. There is a noticeable evolution in hull form from the B-girls to the Skipjack, Thresher/Permit, and Sturgeon classes, leading finally to the LA class and the Seawolf and Virginia classes. With each class of boat built, they learned more, and improved on the capabilities of the previous designs. In some cases, the improvements were applied to a group of boats, such as the "stretch" 637s and the 688I (3rd-flight) boats.

You can see a similar evolution in the SSBNs. The Washington-class boats were Skipjack hulls converted during construction, to get the Polaris missiles into the fleet. Later classes were fully designed as missile boats, evolving not only with the state-of-the-art in hull design, but also to accommodate the increasing size of the missiles they carried.

Most of the Single-boat classes were experimental - Nautilus and Seawolf, Triton, Narwhal, G.P. Lipscomb - testing new propulsion plant designs. In some cases, a boat originally designed as part of a class was extensively modified, either during or after construction, such that it became a class unto itself, ala the Regulus boats Tunny, Grayback, Growler, and Halibut; and the Special-Ops mods for Grayback, Halibut and Parche (and now Jimmy Carter).

3.  Some of the L.A. class subs were decommissioned even though they are
newer than ones that are still operational. Why would the oldest subs not
be decommissioned?

When a ship is decommissioned is not a function of when it was commissioned.  It is a complex function that amongst other things takes into consideration the cost of continued service, specific changes made to the boat during its lifetime, DoD budget cuts and operational directives, etc.  Some boats which one could make a case for continued service are decommissioned after a relatively short service.  For example the decommissioning of most of our fleet boats after WWII.

Without naming names, some of them were involved in incidents that made their continued service 'uneconomical'.  Also we were in a crunch to find the money to build Seawolf class submarines.  The cost to refuel a 637 or 688 was ten times the cost of inactivating (a polite way of saying retiring) them.  Then the Russians gave up and parked their fleet and everyone told us that we didn't need a submarine force any longer.  That was a very hard battle to fight since we had already started down the slippery slope of getting rid of perfectly good submarines.  We had to cancel the Seawolf class and come up with the Virginia class to build highly capable submarines that didn't cost as much as the Seawolf.

Further, it sort of depended on the boat. Some boats with lower hull numbers spent a lot of time in the shipyard, so had less time on their hulls and more reactor core left. It also depended on their materiel condition, and where they were in the upgrade cycle - boats that had just come out of a shipyard availability for upgrades and alterations were less likely to be retired than boats of similar age that were in need of major repairs or had not yet gotten the upgrades. Plus, when it became clear that the Seawolf class was only going to be 3 boats, and the follow-on Virginia Class boats were not going to enter the fleet as soon as expected, the Navy started looking at refueling some of the 2nd-flight LA boats to maintain the force levels.

For instance; the USS San Francisco SSN-711 was about a year out of refueling overhaul when she hit the underwater mountain destroying her bow, had that happened before she was refueled they probably would have scrapped her in a heartbeat, and refueled another boat in her place.

 4.  What do the designations mean like:         

A.  SS
B.  SSN (nuclear apparently)
C.  AGSS (AGS-579)
D.  SST  (SST-1)
E.  SSK/SST  (SSK-1/SST-3)
F.  SSR/SS (SSR/SS-572)
G.  NR-1  (Nuclear Research?)
H.  SSBN (nuclear-ballistic sub I guess)
I.  SSBN/SSN  (SSBN/SSN-642 and -645), DITTO -609. 610. 611 and 618 for
Ethan Allen CLASS)
J.  SSGN Conversion

The type designations used for submarines and their meanings are:

 AGSS              Auxiliary Submarine formerly AGSS, a.k.a. Auxiliary General

AKSS              Cargo Submarine (ex-ASSA)

AOSS              Submarine Oiler (Symbol formerly AO(SS), ex-SSO)

APS                 Transport, Submarine (Later SSP)

APSS               Transport, Submarine (ex-ASSP, reclassified LPSS 14 Aug 68)

ASSA              Cargo Submarine (ex- SSA, later APSS)

ASSP               Transport Submarine (ex-SSP, later APSS)

LPSS               Amphibious Transport Submarine (ex-APSS Reclassified 14 Aug 68), a.k.a. Landing Platform

SC                   Cruiser Submarines

SF                    Fleet Submarine, First Line

SM                  Mine laying Submarine

SS                   Submarine (ex-Submarine First Line), a.k.a. Submersible Ship

SSA                 Submarine, Cargo (Later ASSA)

SSB                 Fleet Ballistic Missile Submarine

SSBN              Fleet Ballistic Missile Submarine (Nuclear Propulsion) SSBN to 1967

·        SSBN/SSN Indicates boats originally designated SSBN which had their missiles removed (due to one of the SALT treaties, and were converted to SSN service until they reached reactor core end-of-life and were decommissioned.

SSG                Submarine, Guided Missile

SSGN            Submarine, Guided Missile, Nuclear

SSK                 Anti Submarine, Submarine a.k.a. Submarine Killer

SSN                 Submarine, Nuclear SSN to 1967 a.k.a. Fast Attack

SSO                 Submarine Oiler (Later AOSS)

SSP                 Submarine, Transport (ex-APS, Later ASSP)

SSR                 Radar Picket Submarine          

SSRN               Radar Picket Submarine (Nuclear Propulsion) (1956-61)

SST                 Target and Training Submarine (Reclassified 1953)

5.  Where did the 6881 class designation come from?  That's an odd name
and there was not a first vessel named or numbered 6881 to begin the class
as is customary.

Actually, it is not 6881, it is 688I, as in 688-Improved. These are the 3rd-flight boats with the VLS tubes in the bow, the forward diving planes moved from the fairwater/sail to the bow, and other improvements.

6.  I thought the German U boats could dive twice as deep as the US fleet
subs (I'm not sure of the Japanese subs.  But the US subs were supposedly
a lot more comfortable (relatively speaking).  Is that true and if the
German boats could go so much deeper, why were the US subs superior?

Have never heard of this fact, unsure of any source here.

Is there any reference that talks about the evolution of these vessels?
Like the first hunter/killer subs and how the Permit class went to the
Tullibee, Sturgeon, Narwhal, etc?  These are guesses as to Hunter/Killers
since I can see from the profile they don't have the deck and conning
tower forward like a SSBN.  And I assume the H/K's started as the need for
"boomers" caused a huge divergence in the operational needs of nuclear
boats for hunting other subs vs. a stealthy missle platform.  Ditto the
seemingly small outward differences of the ballistic missle subs that have
had a LOT of different classes.

This question is fairly well answered in the response to #1 & 2 above.