RE: Modem strangely answers my phone, when ppp is not connected.
At a console please run:
% ps aux | grep -i getty
and post the output.
Two possibilities I can think of off the top of my head are;
1. that your system has been configured for dial-in access, in which case
mgetty or some similar program will be running (hence the above); or
2. your modem has been set up to automatically answer. If this is the case
you will need to check your modem documentation for the proper way to disable