this is not a question regarding a particular problem, it's rather asking for your opinion. Let's say we have a website. It is not visited significantly more often by users of any of the fractions, so statistical argument should be left aside. Which share icon to use when grouping share options? Or maybe should it adapt to the OS user visits the site from? And can we transfer it anyhow to the desktop, so that users who got used to particular representation on mobile can see it also on desktop?
Which share icon to use when grouping share options?
If sharing is important for your business, then use the sharing icons users will recognize. The faster a user finds her favorite social network icon, the likelier she will post the link. Any cognitive load, as in using unfamiliar icons, will decrease the willingness to share content.
That means that you should use the icons recommended on each social media. Share, tweet and pin it as long as the user gets what she expects while clicking the buttons. One example of how this could work, and be nicely grouped is Mashables' articles where sharing activities comes just below the headline but before content:
Or maybe should it adapt to the OS user visits the site from?
That is of course an option, but having real icons instead of the anonymous iOS share or an Android share icons are preumably better. And since this is mobile web, users more familiar with their own mobile web browser sharing buttons will use those instead. An exact duplicate icon on the web page could be confusing.
And can we transfer it anyhow to the desktop, so that users who got used to particular representation on mobile can see it also on desktop?
That's the tricky part, and what is the real argument for using the social medias recommended icons instead of iOS or Android icons. You will not be wrong using standard social media icons, but you could go wrong using iOS or Android icons. Safety first.
After reading this article I was wondering if there could be a single winner in the case of sharing in case someone wanted to represent it abstractly and to group all the share actions as you mentioned.
After some deep thinking on what sharing would look like, it does not seem to me like two children sharing a chocolate, referring to the icon where you have two hands. Nor is sharing whispering in someone else's ear; this is gossip.
Sharing is take something that is mine and has value and sharing it with a crowd. This is when the image of a person throwing something valueable like money to the crowd came in mind.
Therefore I must conclude the "Y" (old android) is the winner and the most suitable icon for sharing