That’s likely a carrier issue and not something specific to your phone. To rule it out, try using your SIM in another phone (say an old one that you keep around for backup) and have an associate call you internationally to see if it goes to voicemail. If it only happens with your regular phone, it’s possibly a phone issue, if it happens with the older phone too, it’s likely a carrier or SIM issue.
Calls going to voicemail can also be related to the load on the cell towers you are around — when at capacity for calls, your phone will not ring and calls will go to voicemail.
Separately, the caller could be using a service like Slydial to go directly to your voicemail manually.
The only way to turn on an iPhone without a power button is to plug it in to power. If it was shut down while connected to a sync cable then disconnect and reconnect for it to turn on.