Suppose
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Start at point A.
walks A→C pointing North the whole time
walks A→B→C pointing North the whole time
When they both arrive at the North pole they will be pointing different directions.pic.twitter.com/UIO7iIDTTU
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I'm not sure what you mean. I don't quite see how acceleration is relevant to the topology.
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There's no contradiction, either in gravity or on simpler non-Euclidean spaces. Geodesics can converge and don't need to do so in an asymptotically parallel way. This aspect is quite static, about the paths themselves rather than dynamics along them
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