No, the show hasn’t been renewed for next season. We won’t know that for several more weeks yet. And yes, the ratings have been picking up a bit so that is a good sign.
The good news is that Fox has announced the air schedule for the second half of the first season. And according to a report at Dollverse, the show will get its full run of 13 episodes. New episodes will air on April 3, 10, 24 and May 1, 8 and 15. There will be a scheduled pre-emption for the return of “Prison Break” on April 17th, but at least we’ll get to see the entire season. And it looks like they should air in the order creator Joss Whedon intended.
So, keep watching and maybe we’ll get that second season….