Vintage omega serial number advice

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This is my first time looking at vintage omega watch. I am now looking at an omega seamaster ref 2736. The condition is good but I have a few concerns and would like to seek your advices

1. The serial number on the case and calibre are different. Case is 8 digit 112xxxxx while the movement is 8 digit 129xxxxx. I saw online 112 should mean the watch was produced earliest at 1947 while 129 means earliest 1950. Is the discrepancy make sense?

2. Ref 2736 I saw online usually it comes with calibre 354. But the one I see now is a calibre 351. But since calibre 354 was launched in 1952. If the watch was late 1940s or early 1950s according to the watch serial no, is it possible that the watch is equipped with the previous movement 351?

3. And for the dial, it looks okay except that there is no ‘Swiss’ or ‘Swiss made’ at the 6pm. Is it common for an early 1950 watch ?

And the offer is not expensive, considering these doubt, will you still take this watch if it’s cheap?

Many thanks