How to set up R7000 as extension of primary RBR50 router for video camera use

> I have a R7000/AC1900 router [...]

   Starting that description at the ISP end might have been clearer.

> [...] to a Hughesnet modem [...]

   Not a very detailed description of anything.  Is it a simple modem,
or a modem+router?

> [...] all the device IP addresses on the R7000 are 10.0.0.x [...]

   And, presumably, other devices are on one or more different subnets?

> [...] What mode do I need to set the R7000 to so that cameras will be
> visible via the internet? AP, Bridge or Repeater Mode?

   If you already have cables (or cable-equivalents) connecting these
things, then, most likely, AP.

   Generally, you probably want one router (so, one subnet).  If your
(unspecified) "a Hughesnet modem" is not a router, then I'd guess that
the RBR50 should be your one router.

   Visit http://netgear.com/support , put in your model number
("R7000"), and look for Documentation.  Get the User Manual.  Look for
"Use the Router as a Wireless Access Point".

   Note that if you need to configure port forwarding to enable remote
access to your (unspecified) "wireless cameras", then that would be done
on the router, not on the R7000-as-WAP.