simply put yes:
communicates with router 192.168.0.1 to go find a page on a website.
request comes out the pubblic interface of your router 18.104.22.168
and off to the website 22.214.171.124
hits the websites router
get'snat'd to an internal address 192.168.0.1 and back.
your client never knows the internel address, only the external (126.96.36.199) of the webserver.
the webserver never knows your client IP, only the public address of your router to respond to (188.8.131.52)
as for the second question:
ok but can you explain what happens when 2 private ips needs to communicate on 2 seperate networks across the glode. lets say 2 different host pcs with similar private ips
if there are firewalls and NAT then don't worry, the clients never see the internal IP's of the other networks.
if you're creating a VPN tunnel in the middle then you need to use separate address schemes since the two sites appear to be a single site, (and you can't have two addresses that are the same on the same rout-able network.