There are no problems I am aware of. The certificate error you experience is okay to be ignored, just add an exception. I don't know why that is happening, as that link works fine here.
Check your email using cPanel to ensure none of the "sent" messages are bouncing back. Some email providers block x10's mail servers due to past abuse. I find using SMTP is easiest-have you considered Google apps?
x10 do not switch users between servers. The only thing you could do is try using a proxy.
Also, the URL you posted is incorrect....try: https://stoli.x10hosting.com:2083/