Yes the online application form is the electronic equivalent of VAF4A. It is straight forward. If there is information you need to go away and find (e.g.details of her parents) you can save your progress, sign in later and continue the application.
This application form is not actually submitted online. After it has been completed and once payment has been made, it is printed off for the applicant to sign and bring along to their appointment. The printed application form contains a payment reference number. So the form provides evidence that payment has been made (and it can't be printed until payment has been made).
There is no online submission of Appendix 2. Once VAF4A has been completed there should be a link to a pdf (I think) of Appendix 2, which again you print off and the applicant signs.
I completed the form VAF4A for my wife by logging into her account. Once printed off she signed it making it her application.
If you complete it remotely for her, after completing it and making payment, save the application as a .pdf file and send it to her to print out and sign, or she can login herself and print it out. I have a saved PDF of our application form. Before making payment, obviously ask her to log in and check all the details on the form. After payment is made I am not sure if you can change details and print it off again
To reiterate, make sure Appendix 2 gets completed (by hand).