IIRC, the deadline to appeal is only 20 days from the date of the ruling, so he'll most likely get right on the appeals procedure. I think he can file a motion to reconsider simultaneously, though.
Yes, the trial court retains jurisdiction over it if it's an interlocutory appeal. If he's dismissed the entire case, though, possibly not.
"29.5. Further Proceedings in Trial Court
While an appeal from an interlocutory order is pending, the trial court retains jurisdiction of the case and unless prohibited by statute may make further orders, including one dissolving the order complained of on appeal. If permitted by law, the trial court may proceed with a trial on the merits. But the court must not make an order that:
(a) is inconsistent with any appellate court temporary order; or (b) interferes with or impairs the jurisdiction of
the appellate court or effectiveness of any relief sought or that may be granted on appeal."
My guess is he probably wouldn't, even if there isn't a different rule that would stop him, though, because it's an accelerated appeal. It wouldn't really help and even his ruling if he reconsidered while the appeal was pending would still be subject to being overruled anyway. So he might as well wait at that point.
Also, he might not even have jurisdiction to reconsider the ruling past the TCPA ruling deadline. Even if the trial court has jurisdiction of the case in general, the TCPA deadline is a hard deadline.
However, if some of the causes of action are still active, theoretically, the trial court could move toward trial on those, including on discovery. Again, there are reasons not to do that, since the defamation claims could be thrown out on appeal anyway, but for instance, there's no specific reason it would be prohibited to, for instance, take depositions from defendants or third parties as relevant. I'm sure Jamie Marchi still knows something relevant to the case even if she's not a party, for instance.