...
How does one connect to the cluster with an Android tablet?
In general you will need an ssh based application. Try ConnectBot available on GooglePlay.
How does one connect to the cluster with an iPad?
In general you will need an ssh based application. There are dozens of ssh clients. Try iSSH. By many accounts it is considered one of the leading contenders.
X Window support info
What is X11 forwarding?
ssh provides a protocol for sending X11 graphics between computers. This option needs to be turned on within your ssh program, such as SecureCRT or ssh, etc. If you use SecureCRT you need to enable X11 forwarding. Look for this option in your SecureCRT preference or global settings.
...