A woman can only become engaged by her will. One who engages a woman against her will, she is not engaged. But a man who they forced until her engaged against his will she is engaged, but there are those who say she is not engaged and therefore it is in doubt. [Rema: If she originally said engage me and he threw engagement money into her arms and said to her: Behold you are betrothed to me, and she shook out her clothing while he was saying so to throw the money from her and said that she did not intend to get engaged and was only joking, even so she is engaged (Moharam, end of Sefer Nashim). They do not go after in the topic of engagement proofs that she did not intend to become engaged. If he took a woman's hand by force against her will and gave her engagement money and she does not throw the money away she is engaged, even though at the beginning it was by force and he gave it to her without saying anything, since at the beginning they were talking about engagement. If he owed her money and she told him, Give me my money: and when he gave them to her he said: Behold you are betrothed to me" and she threw the money away she is not engaged.
One who marries without witnesses, even with one witness, is not married. And even if the two of them agree in the matter. And even if he married her in front of one witness and then married her in front of another witness, this one not in front of this one, she's not married. Rama: And some are stringent if he marries in front of one witness (Tur in the name of the Sma"g) if the two of them agree; but if one contradicts the witness, don't worry (so did the Rashba"tz explain according to the Sma"g). And in a situation of anchoring [she'll be an "agunah"] and pressure, [you can] rely on the lenient opinion. And there is no difference whether the witness says she was married in front of him alone, or if he says she was married in front of two and he alone saw, and the others say they didn't see (Beit Yosef, and similarly it's implied in the Responsa of the Rashb"a). And similarly if he marries in front of two, and one of them is a relative, it's as if he marries in front of one witness. And see later on Siman 47:3.
It is necessary for the betrothing man and the betrothed woman to see the witnesses, but if those two [witnesses] saw them through a window, and they could see, but were not visible to him or to her, she does not require a *get* [bill of divorce] from him. Rem"a: And even if they witnesses heard her saying that she was accepting the betrothal, she can say, "I know that there is no betrothal without witnesses, and I intended to play with him" (Riva"sh - Siman 266). And [this is true] only if she said that she only intended to play, but if she denies that she accepted at all, and the witnesses testify that she accepted, she can no longer say, "I intended to play," and it is a betrothal (Mahara"m Padawa - Siman 32).
Marriage in front of witnesses, even if he didn't say, "You are witness", the marriage is effected. Rama: Even if witnesses were specified, others can see the act and testify (Rivash Siman 479). The witnesses need to see the actual giving to her hand or her property. But if they didn't see the actual giving to her hand, even though they heard him say, "Marry me with this certain object," and after ward she walks out with it under her hand, it is not a marriage until they see the actual giving (Responsa Rashba Siman 680). One cannot go after guesses and logical proofs in this regard. One who marries through a hole in the wall, such as she stretching her hand through a hole and someone comes along and puts into it [an object for] marriage, and the hole is narrow, and it is impossible to see the moment of marriage, and she says she didn't hear that she was being married, she is believed since she could have said [a better claim] that it wasn't her hand but it was someone else's (Rashba 1179), as long as there aren't witnesses which prove her wrong. Any testimony that cannot be examined in a court of law is not considered testimony for marriage [either] (Inferred from the Mordecha at the beginning of laws of money). Therefore, even if witnesses say outside of a court of law that she is married, the court of law can respond to them saying "She is NOT married." And so too the opposite case (Responsa Rashba brought by the Bet Yosef). Marriage witnesses do not need to be scrutinized and inspected if there is no reason to suspect trickery (Rashba 1209). If they find it wrotten in the document, "A certain man married a certain woman" and witnesses signed it, when the document no longer available, the marriage is not suspected (Hagahot Mordechai to Kiddushin). And it is not like those who are stringent about the matter (Makarik Shoresh 74).
Someone who marries using witnesses who are invalid on a Torah level, there is no marriage. But witnesses who are invalid on a rabbinical level, or the witnesses are invalid according to the Torah on a doubtful level, if he wants to enter [into marriage] he should go back and marry with kosher witnesses. If she does not want to enter, he needs to give a divorce document for the doubt. Even if the woman denies and says, "I was not wedded," we force him to give a divorce document. So is the law with all marriages of dount, if she wants to enter he goes back and marries definitively, and if she does not want to enter she needs a divorce document from him because of doubt. And if another comes and marries her, she is now married to the second on a doubtful level, and she needs a divorce document from both of them, or the first one must divorce and she can marry the second. But to divorce the second and marry the first, no. Rama: Someone who is suspected of sexual impropriety (arayot), even if there is no witnesses of the sexual act, but it is just a suspicion (Tosafot and the Rosh), he is invalid for testimony for woman's issues, whether for marriage or divorce (Rambam). Someone who marries using witnesses who are invalid on a Torah level because of their wickedness, such as in front of rapists or other wicked people, some say the marriage is suspected to have taken effectm for perhaps they repented (R"Y Mintz Siman 11, and so in Orchot Chaim in the name of Rashi). And some are lenient (Bet Yosef, and Maharam Padawa Siman 37). However, those who are forced to convert through fear [of reprisal], and they cannot get out of it, but in hiding keep the commandments, they are kosher witnesses (Rivash Siman 11). Some say that that which we say that one who marries using those who are invalid witnesses on a rabbinical level are suspected to have effected the marriage, this is for a Torah-level marriage, but a rabbinical marriage, and the witnesses are invalid on a rabbincal level, the marriage is not suspected as haven taken effect at all (Bet Yosef in the name of the Harashbetz in a Responsa).