According to the newish Star-Telegram politics blog, the writ of mandamus regarding Wendy Davis' ballot eligibility will be heard by the Second Court of Appeals on January 23. The court order setting the date for oral arguments is here (PDF).

In the case of LaRhonda Torry here in Houston, the First Court of Appeals has received a response to the original filing from respondent Gerry Birnbirg, but has not set a hearing date. You can follow that case here. We'll see what happens.