1. I can't know why your old form stopped sending emails.
2. With BV10, you can process your form in two ways:
a. Through an external script, as you were doing with your old for. In that case, a piece of php code had to be embedded in your "Thnak you" (or action) page.
b. The new way: BV 10 will embed AUTOMATICALLY the necessary php code, not in the thank you page anymore, but in the Form page itself. You CAN'T see this code whilst you are in BV, it is embedded at the moment of publishing. This new code is by FAR better than the old script used up to BV9. However, the form page now needs to be PUBLISHED as php.
You don't save it as php, you save it simply with it's name (contact) BUT you need to go to Page Properties, and set the Extension of the Page when published to be php instead of html.
Also, your Thank you page now becomes a simple page with a thank you message, there is no need for it to have any code in it, NOR it needs anymore to be php.
As you see, things have been inverted: in the past the form page could be html but the thankyou page needed to be php, now it is all the other way round: the form page MUST be published as php, the thank you page can be html .
And YES, you CAN publish (not rename) your index page as php, but you also need to go to connect to your site with FTP or File manager, and DELETE the index.html file from the site, or it will prevail over the new, php one.
if your menus had the homepage link simply as
http://www.yoursite.com then you need not touch your menus, if, instead , your homepage in your menus was provided as
http://www.yourdomain.com/index.html , then you should change the menus to have
http://www.yourdomain.com/ . No need at all to add the "index.php" at the end.