No, but you're confusing us with sentences like the above... FSD Beta is NOT Navigate on Autopilot. Navigate on Autopilot is a separate software stack that runs when you're driving on limited access roads, ie, interstate freeways and the like. Its functionality set is completely different than FSD Beta, which is used everywhere that NoA isn't used, ie, everywhere except limited access roads.
Some of the things you are reporting have some of us thinking that you haven't correctly enabled all of your FSD Beta functionality after you received the software. You need to go into the appropriate settings and turn FSD Beta ON before it'll work. This is explained in the "welcome" email you received. So please double check your settings, and give the FSD Beta documentation a read through; it'll make it much easier to use the software, as well as what you can expect from it.