Yes, the word for "customer" or "client" is really "cliens." "Emptor" is a "buyer" or purchaser. They introduced "cliens" to us earlier in the course, but now want "emptor," which is actually a bit different, and incorrect imo. If you try writing "Cliens canem meum emere vult" in fact, it is marked as incorrect. I have probably sent thirty reports in about this! I think I'll ask a friend of mine, who is a mod, what their reasoning is.
There are heated discussions about the pronunciation of Latin, and of course, nobody can really know how they spoke. It certainly is natural to elide a final consonant into a following vowel. I know of no modern language where one would make a glottal attack on a vowel placed after a consonant in a sentence.