Learn English – Meaning of “-esque”

As an adjective, empiric means empirical. It can additionally be used as a noun, while empirical cannot. So as long as you're using it as an adjective, then yes, empiric and empirical are interchangeable. (I think the -ical version usually sounds better, but that's just personal preference.)

Note that empiric was originally a noun only. The suffix -al was added to make it into the adjective empirical, but empiric itself came to be used as an adjective as well. Since this happened over four hundred years ago, and since both words have continued to be used with the same meaning, you can use whichever you like.

I should add, though, that empirical is more common in most contexts. (This probably has something to do with why I think it "usually sounds better", as I wrote above.)

No, -que and -ck are not interchangeable in general.

The final -que pronounced [k] in English is only found in words of non-Germanic origin, usually French. In French, this is a very common word ending. In English, -que- is naturally pronounced [kwi] (the vowel may vary depending on what follows the e), but when -que is at the end of a word, it is pronounced in a French-like way.

In the word cheque/check meaning a method of payment, both spellings are possible. The meaning is the same. As usual, the French spelling is the standard one in British English while the more phonetic spelling is the standard one in American English. When check means verify or verification, it is always spelled check.

Most other words that end in -que cannot be spelled another way. In fact, while there are several other -que/-ck pairs, I can't think of another one where the two can have the same meaning: others are just different words that happen to have somewhat similar spellings and pronunciation. (Not identical pronunciation: as a rule, the vowel before -que is long and stressed, whereas the vowel before -ck is short.)