Learn Italian: Non essere così suscettibile, era solo uno scherzo!

In Italian, the negative imperative for the informal 'you' (tu) is always formed using non plus the infinitive of the verb. If it were a positive command, it would be the irregular form sii (be!), but for the negative, it stays as the infinitive non essere.

Does suscettibile mean the same thing as the English word 'susceptible'?

They are related but often act as false friends. In Italian, suscettibile usually describes someone who is 'touchy', 'thin-skinned', or easily offended. While it can sometimes mean 'susceptible' to a condition in formal contexts, in everyday conversation about someone's personality, it simply means 'touchy'.

Since this lesson is about the verb avercela (to be angry at someone), how could I use it to say 'Don't be mad at me' alongside this sentence?

You could add Non avercela con me! (Don't be mad at me!). Just like non essere, it follows the negative imperative rule for the tu form: you keep the infinitive of the base verb avere, drop the final 'e', and attach the pronouns ce and la to make avercela.

Why use the imperfect era instead of the passato prossimo è stato for 'it was just a joke'?

The imperfect era is used here because you are describing the nature or characteristic of a past situation, rather than a specific completed action. You are explaining the essence of what the situation 'was', making the descriptive imperfect the most natural choice.