My 2002 protégé ES has begun doing weird electrical thing. The cruise control will disengage when I turn on the directionals, or lights, or vent fan. It does not do it all the time however.

Also, the alarm has been acting strange. Yesterday I came out and the security light was blinking faster than normal and not as bright. I got in and no alarm went off but when I inserted the ignition key and tried to start it, the only light I got on the dash was a dim oil pressure light.
When I stepped on the brake pedal, all my dash lights came on like I had full power. The car would not start until I got out, armed and then disarmed the alarm. This has happened twice so I stopped arming the alarm.
Any ideas what is going on?