> we fast for 2 meals on the first Sunday of every month.
Not everyone does (pregnant or nursing women, or the sick, for example (edit: or people who just don't wanna)), and not everyone fasts for that period of time. Some people in different roles in the church (what non-Mormons might call a prophetic / visionary role) are encouraged to fast more often.
> For Mormons, food and drink is abstained starting Saturday night after dinner until Sunday night's dinner.
Many will frequently shift their fasting times. I do. Just posting this because I often talk to people who tell me exactly what I believe, because they read it online.
> In both cases, Mormon fasting and participating in Ramadan, I can say that I have noticed personal health benefits
I'm just another anecdote, but I have noticed no personal health benefits. What I would call thinking or meditation benefits, perhaps. I have frequently felt relief that while I may have overeaten the day before a fast, my belt will usually fit nicely on the following fast day. ;)