Tenant Check

I’m a first time landlord and letting my property through an estate agent providing fully managed service. I would like to know if I can request for tenant’s right live in UK, credit referencing, and previous landlord reference letters from the letting agent? Also I would like to know what are the checks that as a landlord I need to carry out to be legally compliant. Tenant is recommended by the letting agent as they are already using the letting agent service.

Tenant’s current situation is – their landlord needs the property back as they want to move back and they are with the letting agents for the past 8 months.

Please can someone help me with my questions ?

Thank you.