lose phone conversation when arming alarm??

yes. system uses phone line to communicate with central station so it has to cut you off. must be sending a opening or closing signal to CS. you could have this turned off if you don't need opening and closings logged at the CS.

Your alarm system is reporting the change in status (armed / disarmed) to the central monitoring station. This is usually done to protect businesses rather than residences. Unless for some reason you want that level of service, you can ask the alarm installer to reprogram the system. One option with most modern alarms is to have the system send a test signal once a day. This is often done in the middle of the night when clients are unlikely to be using the phone.