Can I continue my save on a new switch with a new game copy
Yes you can. You will need both Switches.
From the Nintendo Help pages:
On the source console:
- From the HOME Menu, select "System Settings" > "Users" > "Transfer Your User and Save Data."
- Select "Next," and then "Next" again, then select "Source Console" to indicate that the content will be transferred from this console.
- Select "Continue," and then finish the following preparations on the target console.
On the target console:
- From the HOME Menu, select "System Settings" > "Users" > "Transfer Your User and Save Data."
- Select "Next," then "Next" again, then select "Target Console" to indicate that the content will be transferred to this console.
- Select "Sign in" and choose to sign in using your Nintendo Account e-mail address or sign-in ID.
- Enter either the e-mail address or sign-in ID associated with your Nintendo Account, and the password, then select "Sign in" > "Next."
On the source console:
- Wait for the target console to be found, and then select "Transfer."
- The transfer process will begin, wait for this process to complete.
- Once complete, select "End" to complete the process.
- If no users are left on the console after the transfer is complete, a placeholder user account will be created.
They also include a helpful video on how to do this:
As for if you can play different saves on different copies of the game, yes you can.