1. Yes—you need to use New-AzureADMSInvitation to add a guest user to your Azure AD tenant.
2. No—Azure AD Join can be used without connecting an on-premises Active Directory to Azure AD. 
3. Yes—when you add a custom domain to Azure AD, you need to verify it by adding a TXT record to the DNS settings of your domain registrar. After adding this record, you can verify the domain in the Azure portal.