I've got a USB mic and an over-ear headphones(with 3.5 and USB inputs), and I want to hear myself while training in apps like yousician. What I do now is I connect ear-pods to my phone, wear them, connect the mic and big headphones to my laptop and forward sound using software.
Is there any device(maybe it's what any mixer can do?) that can take sound from a USB mic, forward it to a phone(USB or 3.5 inputs) as well as to headphones and also forward sound from the phone to the headphones?
What you're looking for is called direct monitoring. There are several options:
Maybe you can turn on direct monitoring in your recording program. This is sometimes also called input monitoring or software monitoring This might be useful if you want to hear your voice with software effects like reverb and compression. The main limitation is your system latency. If it's too high, the delay of the sound will make recording impossible.
Some audio interfaces offer low latency or zero latency direct monitoring. However you can't connect a USB microphone to an audio interface - you need a "regular" microphone with analog output. A good audio interface would also make it easier to setup low latency software monitoring, or blend software reverb with directly monitored sound.
Mixers give many possibilities for signal routing. Again, you need a microphone with analog output, not a USB one. Some mixers have built in effects, which you can use for monitoring. Finally, you need an audio interface to connect mixer to the computer. Some mixers have audio interface built-in.