Ckurriemi75 Hello,
Yes, you can stay in the RE train in Chiasso, no change is required in this station, and take the EC from Lugano.
Yes, you must make a check-in in Italy. You can also install the Trenitalia app on your mobile phone and import the ticket with its number and your email-address.
It will be possible to make the check-in on your phone before departure and show the QR code in the app.