Since Rogers is a GSM carrier, you should ask them about trying to replace the SIM card. That can certainly cause issues like this. If that doesn't work, you'll want to do a backup and restore to see if it's a software issue. This is very unlikely to be a hardware problem with the phone itself.
Settings > General > Reset > Reset Network Settings may resolve your call and texting issue... start there.
Basic troubleshooting from the User's Guide is reset, restart, restore (first from backup then as new). Try each of these steps in order until the issue is resolved.
Also, try simply reseating the SIM card as that may resolve your connectivity issues.
The charging issue could simply be a dirty dock connector.. try cleaning with a soft, dry brush. It could also be a cable issue... try a different cable.