Common Law Marriage Requiring a Get
Lemaissa, what is the status a common-law marriage, one where a couple is living together in an exclusive relationship, or are even civilly married, but are not formally married with chuppa v'kiddushin -- are they considered married? R' Yosef Eliyahu Henkin (Peirushei Ivra 4 &5) says that such a couple are halachikly married and if their relationship ends, the man would need to give a get to the woman. R' Moshe Feinstein agrees that the woman should not remarry without a get. See Igros Moshe E"H I 74 where he quotes R' Henkin's opinion but rejects it, and see Igros Moshe E"H III 23 (and R' Moshe discusses it other places as well; he says R' Henkin would agree no get is needed if there was a Reform wedding, see E"H III 23). I'm mentioning this not regarding the permissibility of such a situation, rather if a dissolution would require a get. (This machlokes is very important in certain mamzeirus shailos, where a mother was previously married in a common-law marriage.) Because of the severity of the prohibition of eishes ish, the couple in such a situation should have a get even according to R' Moshe. However, absent a get, we will not consider the children of a woman who remarried after a common-law marriage to be mamzerim, in accordance with R' Moshe's psak. Note: see R' Moshe's teshuvos for the exact situations. Some of his statements may not be applicable to certain cases and certainly should not be understood that his teshuvos, or my bringing them here, as blanket statements.
To the Rambam there is no pilegesh to a non-melech. The Ramban permits it theoretically, but practically even the Ramban holds you couldn't have a pilegesh because she is not allowed to go to the mikva for her tumas nida since she is not married (as brought in the Rivash 425). Many bring Teshuvos HaRan 68 as allowing pilegesh. However, that case is a) already bidieved; we're not pasuling her more, we're only saying she was pilegesh and not an adulteress, and b) the main thrust of that question was does she need to wait 93 days to remarry or not. The question wasn't asking if she's allowed to be his pilegesh in the first place.