This following information is copied from the Texas statutes, as found via the State Resources section of this site. It answers the questions of "If a (male) minor chooses to marry upon his sevententh birthday, does he need one parental signature, or two?" I believe that, except for your last question, it answers all of your other questions, too, as no difference in an underaged married person's rights vs an adult person's rights are mentioned.
To answer your last question, I'll make a separate post and provide you with the Texas Statutes for the requirements to annul the marriage of an underaged person.
SUBCHAPTER B. UNDERAGE APPLICANTS
§ 2.101. General Age Requirement
Except as otherwise provided by this subchapter or on a showing that a prior marriage has been dissolved, a county clerk may not issue a marriage license if either applicant is under 18 years of age.
CHAPTER 2. THE MARRIAGE RELATIONSHIP
SUBCHAPTER A. APPLICATION FOR MARRIAGE LICENSE
§ 2.001. Marriage License
Added by Acts 1997, 75th Leg., ch. 7, § 1, eff. April 17, 1997.
§ 2.102. Parental Consent for Underage Applicant
(a) If an applicant is 14 years of age or older but under 18 years of age, the county clerk shall issue the license if parental consent is given as provided by this section.
(b) Parental consent must be evidenced by a written declaration on a form supplied by the county clerk in which the person consents to the marriage and swears that the person is a parent (if there is no judicially designated managing conservator or guardian of the applicant's person) or a judicially designated managing conservator or guardian (whether an individual, authorized agency, or court) of the applicant's person.
(c) Except as otherwise provided by this section, consent must be acknowledged before a county clerk.
(d) If the person giving parental consent resides in another state, the consent may be acknowledged before an officer authorized to issue marriage licenses in that state.
(e) If the person giving parental consent is unable because of illness or incapacity to comply with the provisions of Subsection (c) or (d), the consent may be acknowledged before any officer authorized to take acknowledgments. A consent under this subsection must be accompanied by a physician's affidavit stating that the person giving parental consent is unable to comply because of illness or incapacity.
(f) Parental consent must be given at the time the application for the marriage license is made or not earlier than the 30th day preceding the date the application is made.
Added by Acts 1997, 75th Leg., ch. 7, § 1, eff. April 17, 1997.
§ 2.103. Court Order for Underage Applicant
(a) A minor may petition the court in the minor's own name for an order granting permission to marry. In a suit under this section, the trial judge may advance the suit if the best interest of the applicant would be served by an early hearing.
(b) The petition must be filed in the county where a parent resides if a managing conservator or a guardian of the person has not been appointed. If a managing conservator or a guardian of the person has been appointed, the petition must be filed in the county where the managing conservator or the guardian of the person resides. If no person authorized to consent to marriage for the minor resides in this state, the petition must be filed in the county where the minor lives.
(c) The petition must include:
(1) a statement of the reasons the minor desires to marry;
(2) a statement of whether each parent is living or is dead;
(3) the name and residence address of each living parent; and
(4) a statement of whether a managing conservator or a guardian of the person has been appointed for the minor.
(d) Process shall be served as in other civil cases on each living parent of the minor or, if a managing conservator or a guardian of the person has been appointed, on the managing conservator or guardian of the person. Citation may be given by publication as in other civil cases, except that notice shall be published one time only.
(e) The court shall appoint a guardian ad litem to represent the minor in the proceeding and to speak for or against the petition in the manner the guardian ad litem believes to be in the best interest of the minor. The court shall specify a fee to be paid by the minor for the services of the guardian ad litem. The fee shall be collected in the same manner as other costs of the proceeding.
(f) If after a hearing the court, sitting without a jury, believes marriage to be in the best interest of the minor, the court, by order, shall grant the minor permission to marry.
Added by Acts 1997, 75th Leg., ch. 7, § 1, eff. April 17, 1997.