Can we apply "Skip to page" logic to JotForm forms?

Also - can we build question logic into the application? (for example, if yes, then next question (#2) shows, if no, skip next question and go to question 3)

It's possible to set conditional logic to skip pages on your form, please check this guide that will provide you more details about it: https://www.jotform.com/help/350-How-to-Skip-Pages-Using-Conditional-Logic 

Also, note that this feature is only available on the "legacy layout", you could make sure that your form is created under such layout by going to the settings tab -> settings section -> show more button -> scroll a bit down and select the "legacy layout" on the form layout drop down. 

I hope this helps.