Well, I'm not a teacher so I won't be able to give you "professional" advice (whatever that means, I think a lot of piano teacher teach by ways of their own experience).
You should always stop playing for at least five minutes when your arms start to feel tired. Soreness afterwards might be a sign of myalgia (muscle pain). If this is caused by playing piano, you're either doing something wrong, or you simply play more than your current physique allows you to (in regards to piano). To make sure your arms won't get tired after playing, you should always have a feeling of flexibility and freedom of movement in your arms. As soon as they will tighten up you will indeed most likely experience muscle soreness afterwards.
I watched your videos and your playing is fine however, and mostly in the nocturne, your movements seem like they're very exorbitant. Try keeping your hands in more closed positions, that is, only move your hand to another positions when your forced to. Also make use of more fingers. In the right hand you just jump around your hand so you can play the notes with more easy and more controlable fingers. I know it is more easy to control your 2nd and 3th fingers, but as soon as you'll play even faster pieces (btw, please don't say songs

) you simply won't be able to play this way.
Now, that's about it. Remember, I'm no teacher and I'm me and you're you. What I'm trying to say with that is that whatever might work for me, doesn't neccesarily has to work for you to. But these are pretty general applicable advices an I hope they'll help you.
BW,
Marijn