Hi Andi,
               1st I am no expert .For your first Q , private_key_password= "your pass" is missing from your eap.conf under tls section may be this is why you have to enter the password manually.

This is how my tls section is
tls {
         rsa_key_exchange = no                                                                                                              
        dh_key_exchange = yes                                                                                                              
        rsa_key_length = 512                                                                                                               
        dh_key_length = 512                                                                                                                
        verify_depth = 0                                                                                                                   
        CA_path = "/etc/raddb/certs"                                                                                                       
        pem_file_type = yes                                                                                                                
        private_key_file = "/etc/raddb/certs/private.pem"                                                                                  
        certificate_file = "/etc/raddb/certs/server.pem"                                                                                   
        CA_file = "/etc/raddb/certs/ca.pem"                                                                                                
        private_key_password = "whatever"                                                                                                  
        dh_file = "/etc/raddb/certs/dh"                                                                                                    
        random_file = "/etc/raddb/certs/random"                                                                                            
        fragment_size = 1024                                                                                                               
        include_length = yes                                                                                                               
        check_crl = no                                                                                                                     
        cipher_list = "DEFAULT"                                                                                                            
        make_cert_command = "/etc/raddb/certs/bootstrap"
}

Try the configuration. This is the default one except private_key_file name changed.

Regards,
Prateek