Is a customary marriage (zawaj urfi) concluded without the guardian's knowledge Islamically invalid, and are the three divorces issued therein affected by the alleged invalidity, and is it permissible to marry the same husband again with the guardian's consent?

This issue is known as "taqlid (following) after action." You acted according to the Madhhab of Abu Hanifa regarding the non-requirement of a guardian (wali), then your husband divorced you three times. Now you wish to switch to the Madhhab of the majority of scholars (jumhur) who state that your first marriage was invalid, and therefore the divorce did not occur. However, the shifting of a follower (muqallid) from following one Imam to another after having acted upon the opinion of the first, if it is in the same issue that still has an effect, is impermissible by consensus according to some Usul scholars. In your case, the effect of the first taqlid remains; Abu Hanifa prohibits this new marriage, as it is a marriage to a woman divorced with a major irrevocable divorce (bainunah kubra) before she marries another man.

Ibn Hajar Al-Haytami said: "It is not permissible for a common person to undertake an action unless he follows someone who permits it. So, whoever marries in a disputed matter and follows one who deems it valid, or if one who holds it valid rules upon it, then divorces three times, then tahlil (marriage to another man) becomes necessary. He is not allowed to follow one who deems it invalid, because that is a combination of taqlid in a single issue, which is absolutely impermissible. If taqlid and ruling are absent, then a muhallil (one who performs tahlil) is not needed."