Hey there!
1. I'm running the stock game with patch 1,4 (no mods), and I have during one campaign sunk at least 4 Yamato in mid 1943, so the answer there is no. However, I'm now in late 1944 and just sank another Yamato, and a large task force seem to contain less capital ships later in the campaign. For instance:
Mid 1943, 2 Yamatos, 2 heavy cruisers, 2 light cruisers, 4 carriers + escorts.
Mid 1944, 1 Yamato, 1 heavy cruiser,1 carrier + escorts.
2. Yes, the ships have weak spots. I know someone here managed to sink a Yamato with one fish only!! And I think he hit it between the main bow guns, I'm not sure.
Check this thread:
http://www.subsim.com/radioroom/showthread.php?t=134824
3. I have no idea about jap subs.
4. You die!!
I think I was hit once by a Yamato (though it might have been simultaneous hits from Yamato + cruiser + escorts), and my hull + all engines were destroyed. The only consolation was that I took him with me to the deep.
Happy hunting!