Skip to a page and prefill fields

Condition 1

If the answer to the field  Would you like to complete the online class registration?  is yes then go to page 2 and complete the registration form. 

Condition 2 

If the answer to the field  Would you like to complete the online class registration?  is No then go to submit. 

I would also like the duplicate fields on pg 1 & 2 like parent name to pre fill. 

I would also like the person to be ale to complete page 2 at a different time. 

That's possible with "Skip to a Page" Condition.

Here's how:  https://www.jotform.com/help/350-How-to-Skip-Pages-Using-Conditional-Logic

To copy fields value from one field to another, here's how: https://www.jotform.com/help/286-How-to-Populate-Field-with-a-Value-from-Another-Field

Let us know should you need anything else.