The underside of the case where the pushers are located looks fine (the cut outs for the pushers vary on the gen cases & polishing also affects the shape/size of the cut-outs). I am not an authority on 78350s (I only use 7835s on my 62xxs), so take this with a huge grain of salt, but that may be an aftermarket bracelet . The stamping looks larger than what I see on verified gens.
Ditto that.
The misaligned minute totalizer hand is likely just loose. Often, these can be repaired with epoxy or you can get a replacement from DW, Phong, etc (but do not be surprised to find the same problem with the replacement hand ). Also, before you make a final decision, can you get a better pic of the bracelet model number stamp on the 1st link after the end link?
I think black is the only color strap that coordinates well with yellow gold without stealing attention away from the main attraction (the gold Newman head). Certainly, not a bright red DeModell like I occasionally wear with my SS '39 when I am feeling Italian
Sly - While anything is possible with vintage Rolex, I doubt they (Rolex) ever fitted a chronometer-rated caliber (1570) to a non-chronometer-rated watch (5513). The principal difference between the 5513 & 5512 is the latter's chronometer-rating. So, if you see a 5513 posted somewhere with a 1570 inside, I think it likely found its way in there sometime after the watch left Rolex.
Always research before you build.
I believe Rolex only ever used the 1570 in the 5512 (the 5513 was powered by either the 1520 or 1530).
As panerai153 said, it is not realistic to convert the 1570 to a 1575. There are about 30+ parts that need to be changed, including the (main) pillar plate, which would likely end up costing you more than the price of the 1575, assuming you are able to source all of the parts.