Q: new iPhone 7 power button on right side getting very hot.

Mine is running very hot as well. Whenever it uses wifi it seems.

The lock button is right next to the processor, so that's the reason why it gets hot.

Try turning it off if it gets too hot, it might damage the battery. (Sometimes, for the first few days of use, a lot of background stuff is going on, like Photos faces scanning)

I am seeing 20% battery drop in 30 minutes of usage. That seems excessive.