Problem sending emails using mail() function

[Destrudo]

Hello Prestarians, I have a problem sending email using mail() function on my Prestashop 1.6.1.0. From day to day, the ability to send e-mails stopped working. After clicking Sends test message i have green confirmation message that email has been sended but... there is not any email. Its worth to mention that I didn't provide any update in presta or server config from a months! Of course I've tried change the email in "preferences->addreses"  but that didnt resolve my issue. Also when I tried to use SMTP option insted of mail() i have:

The SMTP connection failed to start [tls:// serv.addr :587]: fsockopen returned Error Number 0 and Error String 'php_network_getaddresses: getaddrinfo failed: Name or service not known'

Is there any possibility to see debug message after clicking "Send test message" to check whats going on?

Any other solution?