LAN PC with same IP than WAN IP
Background
After reading about network ranges recommended for private and public networks both in random pages, and the RFC 1918 I was wondering whether it would be much of a mess when a private lan PC has the same IP than a random public IP.
One problem is that the WAN IP address wouldn't be reachable, but maybe there are more reasons behind.
Obviously, the LAN IP won't be visible on the WAN.
Question
Would we have communication problem if a computer on the LAN has the same IP than a computer on the WAN? (Being for example, that we configure a lan network on 191.xxx.xxx.xxx)
If you own the address range, and it is globally routed to your network, then you can do whatever you want with it. The distinction between "WAN" and "LAN" is fairly thin.
If you're using addresses that are not yours, it will work to some extent, but can definitely cause a few problems... but only for you, and not for the legitimate owner of those addresses.
maybe once the request leaves the network it would actually get to the host?
It might – assuming your ISP doesn't do any spoofing protection. (And many do, because address spoofing is very commonly done to perform DDoS attacks, so an ISP would definitely pay attention to it.)
But even if it gets to the host, you have another problem: the host will not be able to send any replies back. (Whenever it tries to reply, it'll end up talking to the real owner of those addresses, who will reset the connection as unknown.)
So in other words, trying to use someone else's addresses in your LAN won't make them "public" addresses (the Internet isn't going to send you packets meant for them) – if you want to interact with the Internet, you will still need a NAT and a legitimate WAN address. So you don't gain anything by using them.
And because the addresses aren't from a private range, your games and apps might think that those are their public addresses (even though they aren't) and that you are not behind a NAT (even though you are). This might prevent online games or P2P software from working.
Finally, using someone else's addresses on your own machines will mean that they'll become unable to reach the real hosts which own those addresses. For example, if you configure your LAN to be 8.8.8.0/24, now you cannot talk to Google Public DNS anymore.