Sometimes the "t" of "est" is pronounced and sometimes it isn't. Can we choose whether to liaise or not when using this phrase?

That's an interesting question Katie,

In the conjugated examples of the lesson , the only one where there's no liaison between the 't' and the 'est' is the 'tu' form and I can't justify why.

You just wouldn't say "Ça t'est_égal" 

There are some liaisons that are compulsory, 

on_a , vous_avez, un_ examen

and some forbidden like after 'et'  

or to sound a 'h aspiré':

des héros, des haricots, en haut.

Maybe a lesson on this would be useful...

Hope this helps!