An idiom is a particular turn of phrase which cannot be translated literally into another language. There are thousands of weird and wonderful examples in English:
e.g. this is a pretty kettle of fish, a sticky wicket, a red herring!
It can be quite fun spotting these in another language and trying to find an equivalent in English that captures the original idea.
Imperatives are commands:
e.g. "Type this up for me, please!", "Let's go!", "Listen, all of you!"
The infinitive is the form of the verb that you normally find in the dictionary.
In English it is often written as the 'to' form:
e.g. to study, to play, to eat.
In Greek, they choose to put the 'I' form: e.g. 'I study' in the dictionary rather than the 'to' form.