There aren't many details on the educations of Jane Austen's male characters, but we do…
Getting a Common Marriage License
In 1753 “An Act for the better preventing of clandestine Marriages” set forth the rules for being married by the reading of the banns or by a common license, including the method of procuring either of these licenses. Most of Jane Austen’s characters would have used a common marriage license as it lacked the public nature of the banns and was easily available to the gentry class.
Under the Act, assuming that their were regular church services held in the parish in which the bride and/or groom lived, procuring a common license was primarily a question of paying a fee; having either the bride or groom live in the parish for at least four weeks before the wedding; and ensuring that a bride or groom who was under 21 years of age either had permission from their father/legal guardian or was a widow/widower.
The Act states that if there were not church services regularly held in the bride or groom’s parish, an adjoining parish could be used.
 I have read that by the time Jane Austen’s novels were published that the English courts had ruled that a mother had the right to be her child’s guardian if her husband/the child’s father was dead. I have not however been able to find that ruling.
Updated October 18, 2015
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I remember reading about the mother. It wasn’t necessarily her, it could be her new husband or a relative who took care of her matters. There was also a magistrate. If a daughter didn’t receive the consent because her guardian (i.e. the new husband) didn’t want to give one, she could plead there. I think she could even if her own father objected, but I’m not sure she’d always be given permission.
The Act states that a bride or groom could petition the Lord Chancellor Lord Keeper, or the Lords Commissioners of the Great Seal of Great Britain for the Time being if there was one or more guardian or mother who refused to grant their consent because they were “Non compos mentis,[*] or may be in Parts beyond the Seas, or may be induced unreasonably, and by undue Motives to abuse the Trust reposed in him, her or them, by refusing or with-holding his, her or their Consent to a proper Marriage[.]”
*Non compos mentis, is Latin for “not master of one’s mind” and according to Black’s Law Dictionary, 7th edition generally means insane or incompetent.
Re your note: “I have read that by the time Jane Austen’s novels were published that the English courts had ruled that a mother had the right to be her child’s guardian if her husband/the child’s father was dead. I have not however been able to find that ruling.”
I don’t know about guardianship over other legal matters, but the 1753 Act itself lists the Mother (if living and unmarried) as a valid source of consent to an underage party if the Father is dead and no other Guardian has been appointed – see Article XI.