Mine slow down for sure. Just monitor it unless you really feel something is wrong. Sometimes my female will refuse food getting close to a shed. My male doesn't too much, but his appetite is not near what it normally is. If it continues, let us know. For me, that only lasts about a few days to a week
Some do, some don't. Mine doesn't, but I know some people's do. Like Kylerbassman said, if it continues for a period of time, then something's probably up.
Here's a quote from an article on GeckoTime by Aliza:
"Many geckos do not eat the day or days before they shed. (Other geckos have been known to pause in the middle of shedding to “chow down”). Observe the gecko carefully to determine whether it is in the early stages of shedding and wait until a day after it has shed before considering other reasons for decrease in feeding."