I'd like to run Termux as root: possible? I'd like to have an SSH, HTTP and SMB server on standard ports on my phone.

There's a way to run Termux as root and have the servers run on privileged ports?

Running rooted Android 7.1 on an unlocked device.
The default su from Termux is simple. When run it brings /system/bin/sh for you instead of Termux's shell (typically bash). To solve this issue, you can install the custom su wrapper for Termux by  

apt install tsu

And then you can run tsu so that your bash and everything is now under root privilege.  

Further information:
Use an editor (like vim) to see /data/data/com.termux/files/usr/bin/su and you'll find that at line 10, it calls exec su $@ directly while in tsu, it performs shell detection and at line 80, it runs  

exec su --preserve-environment -c "LD_LIBRARY_PATH=$PREFIX/lib $ROOT_SHELL"

to preserve the Termux enviroment.