Can we hide the questions that are toggled from the “if yes”, “if no” in order to only show the questions that should follow?

Yes, that's possible through conditional logic. You can choose to show certain fields only if a condition is met (for example, only if an option on a radio button is chosen), otherwise they will remain hidden.

Please read this guide for more details http://www.jotform.com/help/196-Hide-or-Show-Multiple-Fields-at-Once