festiva issue

Hi.
I bought this little thing at an auction, as is. It ran home fine,
but the idle and moving was extremely rough. then this morning, about
19 degrees out, it started up fine, but would not shift out of high
gear, then died, would not turn over. I let it sit for about 10
minutes, and it started up fine. I figured out that I need to let it
warm up awhile before driving. But then, whenever I slowed to a stop
at a light, it would sputter and die. I put in in park, and it starts
RIGHT back up. And then it would stop just fine. Is this a fuel
filter issue??
NRMays