Welcome. I'm also fairly new here but here goes:
1. For day 3, are you supposed to do them in order? For example, if you stall after doing a few pull ups, is it ok to go do some push ups and squats and come back later, or is the program designed for all the pull ups to be done straight in a row (which is what I've been doing)?
I believe you should be doing them together in a set and it might
even be less effective if you don't. That being said it's about making progress more than following a program. Maybe for you breaking them up into smaller pieces can get you started until you progress to doing whole sets of them. If that is the case then I say go for it.
2. When doing alternatives, the guide says 3 alternatives is equal to 1 regular. Does this mean I should be doing 30 alternative pull ups (which is also what I've been doing) or 10 (the official guide number)?
That is correct.
Overall, it's about making progress. The program is a guide and it was designed by someone who knows more about this stuff than either you or I but If you are making progress then you are doing good. You'll get better as you go along.