Why is the bad CRC?
What is distro_bootcmd and where can I find the boot command for each board?
The /proc/cmdline is empty, does it mean the kernel command is empty? If not, where can I find it?
Does OpenWrt use initramfs like a linux distro and how does it mount the rootfs?
Well, you are accessing it from the OS and not the bootloader console. It also seems incomplete (see below).
It would be another U-Boot variable that doesn't show in your output. It would have the syntax to boot your router from the flash/TFTP/etc.
In the same location (but not sure why it's not displayed) or at the U-Boot console using the printenv command. This may differ for different bootloaders (depending on device/board). You can likely access U-Boot over serial and see the environment.
It's not clear what you're asking. In any case, routers are embedded devices, the OS is built to specification of the specific device. U-Boot is not like GRUB or LILO - in the sense you seem to be looking for Kernel command line parameters.
OpenWrt kernels are almost always built with hard-coded cmdline; they ignore any command line passed from the bootloader. The overall philosophy is to not trust the bootloader to do anything other than to uncompress, load and launch the kernel image. This is because many routers have bootloaders that were only developed enough to uncompress, load, and launch the stock firmware-- extra functionality that uboot might promise is often broken.
So as long as your device boots, there is no point mucking around in the bootloader.