Arrow pointing away: make sure you have a SIM card inserted and the phone switched on. Go to Phone menu, click on top right corner of screen to bring up the context menu, select "Preferences & Accounts". A new card will open up and update all your network related settings. There will be a setting for "Call Forwarding". If it is "ON" slide it to "OFF". In case it is "OFF" then slide it to "ON". Come out of menu. Reboot your phone. After it comes back on, go back to Phone preferences and slide phone preferences to "OFF" again. Hopefully this should reset the errant behaviour.
Repeated charging signal: There is either a loose connection between one of the following -
1. Your main electrical outlet and the charging plug.
2. The micro USB plug and your Pre.
3. The cable is faulty.
Are you using the original OEM cable and USB to power plug converter? Some 3rd party converters do not have a compatible ratings and result in odd charging behaviour. I had one which would make my Pre touchscreen go haywire and give off intermittent charge on and off alerts when charging with a third party plug. As Cantaffordit suggested plugging cable into a PC to test charge should help to eliminate possible causes.
Hope this helps! Oh and welcome to P|C and the wonderful world of webOS :-)