"iplink: applet not found" error when trying to change the MAC adress
There's no such command. You want to use ip link, with a space in between.
You might want to look up (under Settings -> About phone -> Status) the original MAC address of your phone. Then issue the command without the interface name first: busybox ip link show, and look for the MAC; you will find the interface name of the wifi adapter, which may very well not be 'eth0'. Mine for example is 'wlan0'.
Then you could try disabling Wifi first, then changing the MAC using the commands on the site you linked, then re-enabling it. It may or may not work - for me, the address change confused the Android settings app and it failed to connect to any network I tried. Don't worry though, everything these commands do are temporary and reverted by a reboot.
You could try searching the /system directory for the configuration file of the wireless adapter and editing that. Mine is at /system/etc/firmware/wlan/prima/, but it's vendor specific and this is an Xperia. Be careful to make a backup of the original, because if you screw this file up, your wifi may not function ever again. This file (or any other file in /system) is not restored at reboot!
You're not going to like this part. You could ask your school to un-blacklist your MAC instead, although they probably had a good reason to blacklist it in the first place. In this case, by changing your MAC, you may very well start an "arms race" which will end up in them whitelisting only their machines and locking everyone else out for good. Try not to abuse their system, and only use it with a spoofed MAC when really necessary.