"ครับผม" it's polite word for men and you can use "ครับ" only. For women use "ค่ะ" EX คุณช่วยพูดช้าๆได้ไหม"ค่ะ" (Women say "Can you speak slowly?") ได้ "ครับ" / ได้ "ครับผม" (Men say "ํYes")

I'm not sure at all. Like I said, I just read it somewhere and I can't even remember where. I've also heard older people say that the term wasn't around before. But, I could be completely wrong. One thing to keep in mind, though, is that period works don't usually use entirely authentic language of the period they portray.

ผม : for gentleman. คะ or ค่ะ : for Ladies. ฉัน : for both men and women.

Mm, are you sure that it's that recent? I'm pretty sure I almost always hear it in period lakorns ;)

That's a great question. As far as I've read, ครับผม is a relatively new development in the Thai language, appearing within the last few decades. But I can't find anything about the origin. Sorry about that.