If a runner has no programs installed can they get past Wotan going through third subroutine, primarily does the sacrifice 1 installed program imply they must have 1 program to sacrifice? What if they don't have any credits and they want to get past the second subroutine?

I would say if you cannot break a subroutine on Wotan, it happens as it is written.

So if you don't have 2 clicks to spend the first subroutine ends the run. If you only had 1 you can't pay 2, so I believe the same would hold true for the pay Credits and trash Program subroutines.

Agreed with Hank McCoy.

Absolutely. What happens if you hit a Pop-up Window

I would say if you cannot break a subroutine on Wotan, it happens as it is written.

So if you don't have 2 clicks to spend the first subroutine ends the run. If you only had 1 you can't pay 2, so I believe the same would hold true for the pay Credits and trash Program subroutines.

Absolutely. What happens if you hit a Pop-up Window and don't have Yog.0 or one credit? The run ends. Why should Wotan work any differently? You either resolve a program-trashing effect, or you end the run.

Interestingly, you CAN save the program with Sacrificial Construct (I checked with Lukas) but you MUST still have a valid target. To suggest otherwise is nonsensical.