How works Link controller?

it has been a long time since i worked with this, but perhaps it can help you.

so something like:

FW - LinkController - rtr isp1
                    - rtr isp2

you can choose yourself which device will do NAT, next to the FW and LC it could also be the ISP router, which might make things easier perhaps. then the LC just has to forward the traffic unmodified.

i don't understand the question on how many NAT you need.

there aren't that many deployment guides for LC i believe, this one shows a rough setup (although also for incoming).

https://support.f5.com/kb/en-us/products/big-ip_gtm/manuals/product/gtm_lc_impl_guide_10_1/solgl_bandwidthlb.html