About your problem, please check whether Sending Mail in your serve is enabled or not.
Please go to System > Global Configuration
Then, in the tab Serve, in the Mail Setting part, please choose Yes for Send mail.
Finally, save and check your site.
You can see the image attached for more detail.
If there is still any problem, feel free to ask us for more help.
About the problem here, please contact your host first to make sure that the sever has been enabled this function.
After that, if the problem remains, please create a ticket, send us your site and admin account and the problem here.