You may be required to take the language test again if the previous one will expire. You should contact Trinity College London for advice.
You would only get exemption through studying to at least degree level and taught in English.
I cannot give advice on JustAnswer.
You were first granted a Tier 2 visa but that visa was not activated and in any event you were granted leave in another route Tier 5 - the exception does not apply from a general point of view. But I suggest you seek legal advice as we can only give general answers on JustAnswer.