Explicate will often be used when you are explaining something complex or philosophically deep. You would use this in academics, politics, finance, etc. It indicates that a very detailed explanation (including reasons why things are the way they are) is offered and that it will be complex. "He explicated the nature of political economy on foreign policy processes." Explain can be used for that same purpose or more common purposes, such as explaining instructions or very basic academic ideas. This may not include deep thinking and understanding of reasons behind ideas. "He explained how to use the new TV control."

explain = you tell someone very clearly about something. explicate = you express your feeling or mood to someone ( but i'm not sure about this ).

Rosia ... but utilise HAS it uses ( haha) particularly when you are stressing the utility of something as in taking advantage of the useability of something.

Yes explication is formal reasoned explanation; used in logic for example, and almost never in speech.

Honestly, I don't remember ever seeing anyone using the word explicate. Just as a general tip in English, whenever you have the choice between a simpler and more commonly used word and a longer, less used word, go with the former. For example, it's better to use the word "use" over "utilise".