In my world, the explanation for Elves being naturally skinny is having a much greater muscle density than their Human cousins, basically causing them to be just as strong but far less bulky and a good bit more susceptible to deep wounds. They also have a lower fat content than Men. Would this at all affect how much food they would need to take in daily, and if it does, would they need to eat more food or less food to keep a good body weight? Additionally, would the race have any special dietary needs or constraints?
Would this at all affect how much food they would need to take in daily
Probably not. Daily energy expenditure is going to be correlated with physical activity. Assuming the same muscle mass and that your elves magical skinny muscle cells are capable of the same things as their larger human equivalents, it seems reasonable to assume they'd need the same amount of energy to do the same job.
They also have a lower fat content than Men
Your elves are going to look pretty ripped.
They're also going to find it harder to swim than humans, and they'll have a rough time of it when faced with serious illness as those fat reserves ain't gonna last long. Presumably they have super elven immune systems to help with that, but they'll still starve and weaken faster.
Additionally, would the race have any special dietary needs or constraints?
Don't see why. Could be just the same as a human, if that's what you wanted.
good bit more susceptible to deep wounds
I don't see how that follows at all. Nobody does well faced with deep wounds. Assuming elf muscles are just like human muscles squished into a smaller package, the same amount of effort will be required to stab or cut all the way through them.