Serviio

Is it possible to access the server outside the local network?

Kinda.

If you are referring to someone using a Smart TV or media streaming player from their home network across the Internet, the answer is no. DLNA does not work across the Internet. That would be possible with a VPN tunnel between your two home networks, but that makes both networks appear as one, so computers on your network can be seen on theirs, and vice versa. Not a good idea security wise. It's also a difficult thing to set up correctly, and unless you have major networking experience I'd say don't even think about it.

If you purchase the Pro version of Serviio, you have a web based media player (MediaBrowser) that can be accessed outside your home network with the proper firewall settings. Most devices with a web browser work with MediaBrowser. Pro also includes an API that supports 3rd party players, such as the Android based Serviigo https://forum.serviio.org/viewtopic.php?f=17&t=6803. These players can be configured to access your server from the Internet as well.

Another noob question :

is-it possible to use KODI with this API or other solution ?
For watch serviio on TV without mobile airplay or laptop, outside the local network.

Kodi works just fine with Serviio, but only on the internal network. It can't make use of the API. You have to have an application written specifically for the API to work over the Internet. The only application I'm currently aware of is ServiGo, which is written for Android phones and tablets. Since the Nvidia Shield runs Android, it's possible ServiGo could work on it and access a Serviio server across the Internet. But the developer would likely have to answer that question.

One other comment about Kodi. It ignores the title sort order that Serviio provides, so if you have Playlists with titles in a special order you only get them alphabetically. Same with the Last Added list. But Kodi on my Shield plays everything I have without transcoding.

Thx for your answers !