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Would you actually build more or just for the UK/USA and Japan which have large amounts of old ships.

Do you mean NZ?
It depends on strategy. But the most probable variant is cruisers - CA and CL. Or maybe submarines.
 
Would you actually construct more lvl I and II ships.

no. I think minimum 3.
On the other hand, if you do not plan to leave Allies, you could use their bases. in this case, you could use old scrap effectively.