Impact of Allied invasion of Norway/Sweden in WWII

Britain had people considering invading Scandinavia OTL before Germany to sever Germany’s crucial trade with Sweden, however Germany beat them to the punch. This seems to create a lot of possibilities.

Can Britain and France convince Norway to stand down?

Do Britain/France have a chance of taking Norway and Sweden with German aid?

Can Sweden and Norway stay out of the broader war if they resist the invasion without German help?

Will they go to German for help?

If occupied successfully with the WAllies, how much does it shorten the war if at all?

If Norway/Sweden are successfully occupied by Britain, does Finland stay put during the Eastern Front?

If they defeat the WAllies invasion and join Germany, what impact would Norway and Sweden participating have on the Eastern Front?

What of Denmark?

How big of a PR blow is this to the WAllies?

If they escape Post War without getting conquered, will this be forgotten, or is it likely to cause long term issues between Norway/Sweden and Western Europe?
 
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