... but without a password, I can't use SSH, AP Mode, and many others...)
you definitely could use ssh w/o password although not recommended. You would have to comment the USB0 in /lib/systemd/system/sshd.socket.
Maybe try ssh'ing w/o pw first and then try setting pw within ssh session (e.g. using "passwd" command)?
After typing "myedison login: root", the line "Password: " appears, and I can't type anything...
How to fix the problem?
Sometimes the USB cable/USB port could be a problem. So try changing the cable/USB port.
Try to use the latest image of Yocto Intel® Edison Boards and Compute Modules — Software Downloads
As you said that you are facing problems with Yocto then I suggest you to try with Ubilinux once and test whether it is working or not. I hope it could work.
Follow these instructions for installing Ubilinux Loading Debian (Ubilinux) on the Edison - learn.sparkfun.com or EmutexLabs
I have faced this kind of problem before and solved by flashing it.
Actually,you did type something,but it's hidden,that is to say ,at this step you should input the password(though u cannot see it),and then press enter.