The 105 days doesn't have anything to do with when the reinstated case has to be resolved--that's just the limit within with the court still has jurisdiction to grant a motion for new trial. As to when your new trial date will be, that's going to need to be scheduled with the court. I expect they'll probably want to expedite things, but that would likely depend on the specific circumstances (like whether there's already been an opportunity to conduct discovery or attend mediation, just how long the case has already been sitting on the court's docket, things like that).
In general, no, there is no time limit within which the Court must reset the new trial. The 105 day limit has to do with plenary jurisdiction, but the setting and trial of cases is left to the discretion of the Judge. Generally, the Court should provide forty-five days' notice of trial for the first setting, HOWEVER this would be a new trial on an existing matter, and not the FIRST trial, therefore my gut tells me that the Court would not be compelled to give forty-five days' notice of the new trial.
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