Is there a PC that costs (also used) less than 300 euro and is suitable for streaming? By that I mean that the PC can play like Fortnite and GTA 5 smoothly for viewers.
I honestly doubt it very much. In the best case scenario, you need at least an eight-core processor for smooth streaming and finding a good system for less than 300 euro is almost impossible
For 300 euro new you can fold it completely, even without streaming the gta5 will not work smoothly.
except maybe on low, and 720p
So I would tend to the i7 intel series as a processor because they are the most suitable for video editing / gaming. As a graphics card, you should buy an NVIDIA, as they provide their own streaming and recording program "shadowplay" adapted to the graphics card. An affordable one is the 1050ti which allows you to play most games in medium-low settings. Ram definitely 16GB. Rest is quite often mainstream so which motherboard which cooler etc.
No, not even needed.
For less than € 300, you might find a computer on which you can play the games mentioned smoothly in FullHD, but at the same time it will not be possible to record the games as a stream.
The maximum I can see will be a PC
has a 4th generation Intel I5 or 6th / 7th generation I3. In any case, a maximum of one CPU with a maximum of four cores / threads, that's not enough to stream, even with the older I7 CPU (four cores plus HyperThreading) there were always frame drops when streaming.
As a graphics card I see a GTX 780 or GTX 960 in the computer
All this is rather the lowest level even with pure gaming without streaming.
What you should have to stream
An eight-core CPU (AMD Ryzen or Intel Core I CPU)
As a graphics card, however, you can also use older or weaker models.
I think the project is rather pointless. You could build a pure streaming computer (on which you do not gamble, but really only want to convert the signal) with the ryzen 5 3400G, but the processor is no longer worth it, so it makes a lot more sense to spend a little more, and screw the ryzen 5 1600 12nm with an extra graphics card