며 can have two meanings. 1) verb ending to indicate something is happening while another is going on. In this case, it's the same as -면서. 2) verb ending or a marker particle (after a noun) to list two things, like "and". This is similar to -하고(nouns) or -고(verbs). The -ing form of a verb you mentioned plays a plays a similar role as (1). For example: 1. 친구는 숨을 헐떡이며 달려왔다 = My friend ran to me, panting. (헐떡이다(v) + -며). 2A. 서울은 한국의 수도이며 문화 중심지이다 = Seoul is the capital and cultural hub of Korea (이다(v) + -며) 2B. 동창 중엔 의사며 변호사며 사업가며 없는 직업이 없다 = Among the classmates, there are doctors, lawyers, businessmen, and anything you can think of. (NOUN + 며). As an enumerator(2A), -며 can list things at any level including the top clauses. For example, - 시험과 면접은 2월 말로 끝났으며 우리는 합격자 발표를 기다리고 있었다. == ... -끝났고 우리는 ... = The test and interview ended by the end of February, and we were waiting for the announcement of who passed - 살며 사랑하며 배우며 = Living, Loving, and Learning.

I know 면 means "if". Maybe if is kind of a deliberate "misspelling"? Other than that, I don't know either ㅋㅋㅋ