Do you have any test equipment. The things you are reporting are not what you would expect to happen.
The problem is that if you just have a meter you will not get very sensible readings if you try and look at pulses. There should not be pulses but for example if the capacitor was not in circuit or you made a mistake with the value there would be pulses at that point.
Also measure the voltage on the base of the second transistor. This should be 0.7V higher that what you see on the emitter.
When you say:-
I get 2v on the triak
Are you talking about the voltage measured at the controller pin with respect to ground?
Basically inside that SSR is just an opto coupler, so in effect the input is just an LED.
You can replace it with an LED ( and resistor ) for testing.