I'm replying to my own message, based on a talk we had with an InfoPath Rep in Microsoft this morning.
1) The issue of the "New Document" button not being available in a Forms library in a Site with FBA \
is solved by enabling "Client Integration" in SharePoint Central Administration for the zone of interest.
a) Central Administration | Application Management | Authentication Providers .
b) Pick the application and the zone of interest and then on Enable Client Integration, set the radio option to YES.
NOTE: Enabling Client Integration in a site with Forms Based Authentication WILL CAUSE interference with other
Office products. (Example: We have seen that trying to access office documents in a doc library will not open the
documents with this option turned on).. THIS IS A KNOWN ISSUE TO MICROSOFT. We do not know if they are
working on it in a Service Pack release or not, and have started the process of contacting them regarding this issue.
2) Once again, deployment or publishing of InfoPath Forms to a SharePoint FBA zone is not possible and this is also
a known issue. The current workaround to publish a form is to extend the SharePoint App to create an NTLM zone, and
then deploy the form to that zone.
I hope this resolves some issues for now.