>>52759
I will give you an answer for each question to the best of my knowledge.
>1) Should the Musashi and Yamato had survived up to the use of the two A-bombs would the Japs still feel compelled to surrender?
The Japs still would have ended up surrending even if Musashi had survived Leyte Gulf and Operation Ten-Go never happened. Both battleships would have ended up in the same situation like Nagato and Haruna, sitting in harbor being used as floating AA batteries or getting sunk in shallow water by the various air raids being done by the USN on Kure and the Inland Sea.
>2) If as 1) but the Japs did not want to surrender would the ships be a primary targets for nuking or would they be considered to high risk or to difficult as targets due to their relative mobility?
The US wouldn't waste a nuke on either ship when they can just send in torpedo planes and get the job done cheaper and with better results than using a nuke. This also lets the US save the few nukes available for use against ground forces and fortified positions (Part of the plan for Operation Olympic was to use nukes to clear out landing areas and the Army was worried if they would have enough nukes ready).
>3) If as 1) but Japan surrendered could they have negotiated better terms of surrender? Could they potentially keep the Battleships on partial disarmament agreements?
Neither battleship was worth anything as bargaining tools when it comes to the terms of surrender. Yes the USN would have loved to get a chance to study them, but you are not going to learn anything game changing from the Yamatos when the Iowas had better radar, fire controls, secondary guns, and AA guns. I am also sure that if either or both battleships had survived the war they would have been used as targets in Operation Crossroads for the same reasons Nagato and Prinz Eugen were used as targets.
>4) If Japan won the Pacific War and the 2 BBs had survived could they potentially have as a long active career ahead of them as the USS Iowa had?
I can see them following the Iowa's post WWII career depending on how events play out in this alternate history. However, even in this alternate timeline I still see carriers being the backbone of any navy and battleships would only be used for carrier escort or shore bombardment duty. Still, I wouldn't mind since that means both ships become museum ships that can be visited without the use of a ROV or submersible.
Both Yamato and Musashi are great battleships and one of the best battleship designs ever made, but they are not wonderwaffle ships that can solo entire fleets. They had their flaws and they, like all battleships, were superseded by carriers once naval aviation was established and perfected. At some point in the future the battleship concept might be re-introduced if ship mounted rail guns, nano-composite armor, and laser point defense weapons become commonplace, but for now carriers remain the backbone of a navy.