Hi there.
You can quickly verify if the eSIM is installed and working by checking if there is a cellular connectivity (indicated in the top status bar). Try browsing via the iode browser (or another app) to see if you have data.
You can use the built in Phone App (bottom left corner in the home menu) to dial out (same app manages incoming calls too).
On adding contact, you’re able to save this contact on device or save it in a cloud account (google is one of the options supported, although not recommended for privacy). Simply choose device only in the contacts storage menu (it shows up once, on your first contact creation).