So here we found some interresting articles on Sony Forums Website:
Registering a device
The first time you use 
(PS4 Link), you must register (pair) a PS4™ system with your system.
The number of PS4™ systems you can register with your system is limited.
- You can register 1 PS4™ system with your system for remote play.
- You can register up to 10 PS4™ systems with your system to use the second screen feature. If you try to register any additional PS4™ systems with your system for use with the second screen feature, the information of the PS4™ system that you have not connected to for the longest time will be automatically deleted.
Registering (pairing) a device
Connect your system and the PS4™ system directly using Wi-Fi, or connect them through a wireless access point to register a device.
Before performing these procedures, you need to do the following:
- Link the PS4™ system and your system to the same Sony Entertainment Network account.
If you have an account that was created on a different device, such as a PS3™ system or a computer, you can sign in using that account.
- If you are connecting the systems directly using Wi-Fi, select
– Werbung –(Settings) > [PS Vita Connection Settings] from the PS4™ system’s function screen, and then select the [Connect Directly with PS Vita] checkbox to set a checkmark.
- If you are connecting the systems using a wireless access point, the systems must be connected to the same network.
- 1.
- On the PS4™ system’s function screen, select (Settings) > [PS Vita Connection Settings] > [Add Device].
A number appears on the screen. - 2.
- On your system, select (PS4 Link) > [Start], and then select [Remote Play] or [Second Screen].
- 3.
- Enter the number displayed on the PS4™ system’s screen, and then select [Register].
When registration is complete, the PS4™ system’s screen is displayed on your system.
After these steps you should be able to see this:
So now we get ready to connect outside 😉
Playing remotely
To use remote play via the Internet from outside your home, you must first prepare the PS4™ and PS Vita systems.
- When using an access point provided by a commercial or public Wi-Fi service, or by a private wireless network, set up your system so that it can connect to that access point .
- Turn on the PS4™ system.
- On the PS4™ system’s function screen , select (Settings) > [PSNSM] > [Activate as Your Primary PS4] > [Activate].
- On the PS4™ system’s function screen , select
On your system, select (PS4 Link) > [Start] > [Remote Play]. When the devices connect successfully, the PS4™ system screen appears on your system.
- On the PS4™ system’s function screen, you must select (Settings) > [PS Vita Connection Settings], and then select the [Enable Remote Play] checkbox to set a checkmark.
- If you enable remote start on the PS4™ system, you can use remote play to wake the PS4™ system from standby mode. On the PS4™system’s function screen, select (Settings) > [Power Save Settings] > [Set Functions Available in Standby Mode], and then select both [Connect to the Internet] and [Enable Turning On PS4 from Network] to set checkmarks.
- In some network environments, the remote play connection might become unstable.
Using remote play via the Internet
You may not be able to use remote play via the Internet depending on your network connection. If this occurs, the following reference information might help you make a connection.
- On the PS4™ system’s function screen, select (Settings) > [Network] > [Test Internet Connection], and then confirm that you are able to connect to both the Internet and PSNSM.
- If your router supports UPnP, enable it on the router.
- If your router does not support UPnP, you must adjust the router’s port forwarding setting to allow communication to the PS4™ system from the Internet. The port numbers that are used by remote play are 9295 (for TCP), and 9296 and 9297 (for UDP). If these ports are unavailable, it might be possible to use ports 9295~9304 (for TCP and UDP). For information about these settings, refer to the instructions supplied with your router.
- If the PS4™ system is connected to the Internet via two or more routers, communication may not work correctly.
He got many problems while connecting, but managed to do it 😉
We found out while we were reading all the manuals and his post, when you disable the ‚Connect Directly with PS Vita‘ checkbox
Than you don’t need to go out or something to test it in your enviorment, so the AD-HOC mode from PS4 is turned off 😉
And ‚STREAMING‘ Mode is not working while you are using Remote Play!
Hope this helps someone, post problems and toughts.
Official Source: http://manuals.playstation.net/document/en/psvita/ps4link/device.html
http://manuals.playstation.net/document/en/psvita/ps4link/viainternet.html
http://www.reddit.com/r/PS4/comments/1rkt0u/if_you_got_ps4_and_vita_remote_play_to_work_via/
