Migration Assistant

Migration Assistant gives you some choices but not very many as shown here:

How to move your content to a new Mac - Apple Support

Migrate Assistant won't migrate any Apple apps, they will be untouched as you already have the new apps.

Be sure to run Migration Assistant when you first boot up your new Mac. After a few screens of Setup Assistant it will prompt you to migrate. The fastest way is to connect a Time Machine disk to your new Mac.

I don't think so. Apple Mail is server based, so as soon as you logged in with your Apple ID, you get all the old mail back. I think your best bet would be to delete the unwanted emails before migrating. Or delete them after if you want to keep them on the old Mac.