While streaming Fortnite on Twitch with my PS4 friend, the stream cannot hear him, but I...

Ah, I completely blanked on the PS4 issue. Unfortunately, the only way to do that then would be to use a capture card connected to a PC. PS4 currently doesn't offer cross-platform play except for Fortnite and Rocket League. If you and your friend are playing
any other game it will be impossible for you to stream from your Xbox and have him be heard in the stream.

In the Twitch settings while streaming you can choose to mute your mic so that your voice won't be heard on your stream. Your friends will still be able to chat with you.

Regarding your second question, even with the microphone on, the twitch stream does not pick up the voices of other people in your party. I actually found this forum trying to find a way to make twitch pick up the voices of my friends as well as my own.

Im trying to get my fortnite party chat to come through stream on twitch

So comparing the settings from a PS4 streaming to twitch and an Xbox One streaming to Twitch isn't the best comparison to ensure everything is working, as settings and options could be different or behave differently on each console. But to be clear, your
friend is on a PS4 streaming via a Twitch/native streaming on the console and not via a PC and capture card? Additionally when you say 'non-xbox' friends, do you mean players on different platforms, or do you mean users on Xbox that are not your Xbox friends?
That can help us determine the next best steps for troubleshooting.

I would recommend reviewing the Privacy and Online Safety Settings for your account. Make sure
settings are there to allow you to share outside of Xbox Live. While there review the other settings and make sure there set to what you're comfortable with, since you're streaming to the internet.

Same with me. I tried streaming Fortnite on Twitch tonight through my Xbox and it also said This game doesn't allow live streaming, and that has never happened to me before.