Can the second player’s “mom” mail a foreign fruit

If you buy a second Switch, you're no longer sharing the same island. There is no cloud save transfer available for the game. There will be a data recovery service available later, but it doesn't sound like it can be used to keep an island in sync between two Switches.

Each Switch will have its own island. You can use local or online multiplayer to visit the other player's island or have them visit yours to play together on separate screens.

https://www.ign.com/wikis/animal-crossing-new-horizons/How_to_Play_Multiplayer#Local_Wireless_and_Online_Multiplayer

There doesn't seem to be way to easily split stacks into stacks of more than 1. However, it is pretty easy to take 1 item of your stack. Simply press A on a stack in your inventory, and choose "Grab 1". It will put the single item in an empty inventory space.

If you're looking to split a stack of 30 into two stacks of, say, 15 each, you're going to have to do it the way I described above. It's very tedious.

Finally, you can use a similar way to split items by dropping them on the ground and picking them up, one by one.