Learn Arabic (Modern Standard): لحظة من فضلك.

In Arabic, there is no direct translation for the English words "a" or "an". A singular noun like لحظة simply means "a moment" or "one moment" on its own. You only need to add the Arabic word for "one" if you want to strongly emphasize that it is exactly one moment, which isn't necessary for this common phrase.

The word فضلك ends with the letter kaaf. How do I know whether to pronounce it "faDlak" or "faDlik"?

It depends on who you are talking to! The attached suffix ـك means "your". When speaking to a male, it is pronounced with an "a" sound at the end: من فضلكَ (min faDlak). When speaking to a female, it is pronounced with an "i" sound: من فضلكِ (min faDlik).

Why does "please" use the word من (from)? What is the literal translation?

The phrase من فضلك is a polite idiom. Literally, من means "from", فضل means "grace" or "favor", and ـك means "your". So you are literally saying "from your grace". This is the most standard way to say "please" in Arabic.

Does the last letter of لحظة make a "t" sound or an "a" sound?