Where are these terrorists coming from if not from Chechnya?
Saudi Arabia & Syria, most likely. The money definitely comes from wahhabists in Saudi Arabia.
They are coming from Chechnya and from Arab Sunni countries (primarily Wahabis). Chechens living outside of Chechnya do not cause much problems (beside part of them involvement in organized crime).
Russians under Yeltsin made a horrible mistake by withdrawing the troops and police from Chechnya in 1990s. It allowed Wahabis to set their base and to channel disorganized separatist, tribal or criminal activities into universal mission.