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It looks like the # of parts a larger file is broken into is totally controlled by your local software that is talking to s3 if my scan of this URL is accurate: https://docs.aws.amazon.com/AmazonS3/latest/dev/mpuoverview.html

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But like others have said s3 request charges are not something I've ever seen have an impact on a monthly bill. If you are worried about this you can likely run a test and just do some deep monitoring on the cost dashboard or set up a custom report with configured spending limits set up

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And ACK!! for your #2 question -- please do not use a backup product with S3 that is not explicitly endorsed and supported by the vendor to use S3 or an S3-compatible backup API. Native object storage is different from the POSIX filesystems or tape/library/robot interfaces they may normally expect to see and use in operation. Like fundamentally different. I can't encourage you strongly enough here that this is a dangerous idea for normal data handling let alone a organizational backup/DR scheme.

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