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AWS has Montreal location, Lightsail costs similarly.

Forget everything and call snowmobile https://aws.amazon.com/snowmobile/

Switzerland - Paris is a short distance (well, relative to the global internet) and very well connected I guess. You can use rclone or any software that works with Amazon S3.

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Google Drive is cheapest option, Amazon and Microsoft cloud are very expensive.

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amazon ses allow you to increase per day sending limit 200 to 50k +

Amazon SES should be good for your needs.

Which provider has better network (Stable, lower pings) around Tokyo area to neighbouring countries?

Looks like only Amazon and Rackspace are supported for S3. Use SSH or Google storage.

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I need deep cold storage cloud server like amazon s3, it should allow automatic transfer from webmin/virtualmin server.

Google and Amazon offer it for free. I don't know about Microsoft Though.

I need a VPS in the UK that works with all streaming services (Netflix, BBC iPlayer, Amazon prime video, etc).

You can get AWS Lightsail with 2TB for $5

AWS Lightsail has okay pricing.

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If you are comfortable with opening up one of your laptops,

But, maybe I just miss-understood what exactly you are trying to build. Maybe all you are looking for is something like Amazon S3? Because there would exist open source replicas for that (see MinIO).