Loaded question...LOL.
Well there are several ways of describing the differences.
Lets look at the first question.
The 4343 has an over arching live presentation. That to my mind comes predominantly from the 2121 10 inch mid cone that has some mild cone break up in the upper mid range and the 2420 aluminium diaphragms which were a bit harsh. The crossover was a first attempt at this kind of 4 way system (not by GT). This could be tempered with a smooth sounding class A amplifier like an Aleph 2 SE 200 watt amplifier by Nelson Pass also popular in Japan or a valve amplifier.
I lived with the 4343 for a long time and I enjoyed it. I also auditioned the 4343 in another forum members home and my impression were similar. It was an excellent loudspeaker for jazz genre. Hence it was well accepted by the Japanese audiophile.
The 4344 is refined in a number of areas. The new 2122H mid cone was smoother improved version of the 2121 mid cone. The 2425 compression driver with diamond surround titanium diaphragm was smoother sounding (the titanium does have a nice presence in the tone that goes well with brass instruments) and the crossover network has better topology. The result was improved driver transitions and improved transient performance. The 4344 Lpads need to be set up very carefully with an accurate measuring kit like REW. Once the pads are properly its the last loudspeaker you will own with the one exception of the model 4345 which was the 18 inch version of the 4344. The 4345 was much larger system. Note the 4344 crossover networks can be rebuilt with better parts like the charge coupled approach resulting in far more transparency. A high quality active crossover will also improve transparency.
The 4344mk11 was introduced in the 1990's. It featured a newer slightly more sensitive bass driver, a newer iteration of the 2122H 10 inch mid cone called the 2123H. This 10 inch mid cane is a bit smoother and a more efficient driver. The 2123H tonality is biased towards a more powder smooth mid range but its not as extended as a mid bass driver. This requires careful crossover transition (see the 4344mk11 network). The 275nd compression driver was new and used in other JBL systems of that decade. it features a lighter titanium diaphragm dusted with acquaplas. This resulted in a slightly more damped presentation making it less live sounding. The horn crossover EQ (title) and slopes were revised to optimise the 275nd response curve. The 275nd compression driver runs out full range with a mild rate attenuation above 8000 hertz. The network was fully re worked with a different take on the driver transitions for the critical listener.
My impressions are of a more coherent, smoother and refined presentation which it is if you measure it properly. A bit less JBL house sound (think snappy, chalky cracking transients) to a slightly more mellow hifi presentation. I also found it easier to adjust as the L pads are calibrated +-1.5 db.
To answer your second question.
Yes it it all at once. Otherwise it gets a bit complicated.
Attempting to clone the 4344mk11 is not straight forward as it requires a dusted one inch titanium diaphragm. A few of us came up diy versions of the acquaplas dusted diaphragms. With some careful tweaking I got the 4344mk11 style of system dialled in nicely.
I would use the 2235H woofer, the 2123H (off Ebay or Jammin Jersey).On the compression contact Ken at
http://www.repairspeakers.com for the dusted 8 ohm 2425 diaphragm and see if he can help you before you make plans.
On your third question I think it would be cool to re incarnate a 4343 baffle as a 4344mk11. Making new enclosures is a lot of work.
Pm me if you need further assistance.
BTW those who have time athome and would like a fun project you can build DIY versions of the Pass Aleph quite easily and it won't break the bank. I found the Aleph had great synergy with the JBLs on the mid, horn, slot array when bi-amping. Go to
www.diyaudio.com and the Pass Forum and ask about building an Aleph 3 or Aleph 30 (50+50 watts). Alternatively check out
www.Audiogon.com