1) Yes, we can say that (regarding your assumption). However, semantically both سلامٌ and السلامُ عليكُمْ (or السلام عليك) are different. But, this topic is at the advanced level -- beyond our scope now.
2) For the greeting and parting issues, I don't know how the Arab culture nowadays is -- but in the Islamic way, we say سلام and السلام عليكم or السلام عليك for BOTH greeting and parting phrases (and not only for greeting). And, I think many Arabs still hold the Islamic way. So, they say "salaam" or "as-salamu'alaikum" at both occasions.