Problem
In essence, attachInterrupt uses a macro called ISR (stands for Interrupt Service Routine) to register a user provided function to handle an external interrupt event.
The issue you are encountering is that ISR also wraps the call to your function with special instructions to clear the global interrupt flag of your microcontroller, and set it again after your function returns. This is a good idea, and almost always what you want, because it prevents the possibility of infinitely recursive interrupts.
However, this behaviour will prevent Serial from working correctly, since it relies on interrupts being enabled to do its thing.
Solution
Although this is the default behaviour, there is nothing stopping you from enabling interrupts again inside your c1_rise function, as in:
void c1_rise() {
val_c1 ++;
interrupts();
Serial.print("C1:");
Serial.print(val_c1);
Serial.print("\n");
}
Alternatively, but perhaps more involved, you can use the ISR macro directly by including avr/interrupt.h, and use ISR(vect, NO_BLOCK) to override the default behaviour.
Of course, you should be careful when overriding the default behaviour --- its there for a reason!
For more details about working with interrupts, I recommend reading this documentation.