No, you do not need to get a wallet for Synergy of Serra.
In fact, one is created for you as soon as you sign up for the website but you need not ever interact with it. It's so simple that your grandparents could play.
Yes. Simply by connecting your wallet via your Account screen, found in the top right of the website, and then using the "Transfer Assets" option on the Inventory page.
The blockchain selected doesn't matter for transferring your assets.
Please see Can I move my Fame?.
If you would like extra piece of mind over the security of your assets on Serra then you can connect a hardware wallet to your Synergy of Serra account in the normal way.
Using Metamask, go to the dropdown menu at the top and select Matic Mainnet.
You can add this network by selecting Custom RPC and enter:
Network Name: Matic Mainnet
Click Save to finish.