Serviio

The server app contains port 23424 and 23524 , not specifying protocol.
Also: in the mean time, I connected the Android client to local IP, it does show how many arttsts there are , and the albums, and the cover, number of items inside...but when entering everything is "No content"
However: the Android client does not fail to already annoy me with ads, is that gone when paying for "pro" version of the server?

Ports 23424/23524 are for MediaBrowser, not the console. For external access outside your firewall, you only need these opened. I don't bother with SSL, so I have 23424 as the only open port in my router. I have both TCP/UDP enabled, although I don't know if both are necessary. Unless you have a static public IP address, don't forget you'll need some sort of dynamic DNS service to get you a consistent URL.

If by Android client you mean ServiiGo, you'd be best asking in the forum that is specific to that app. The Serviio developer is not the person who has created or maintains that app. See this location in the forum for help with ServiiGo: viewtopic.php?f=17&t=6803

The Pro version of Serviio is required for ServiiGo (and MediaBrowser) to work, but it has nothing to do with any ads in the app. As I said, they are completely different products.

Dan is correct.

Technically you only need port 23424/TCP for http or 23524/TCP for https. I do not have UDP open...