Is it permissible to give multiple mudds (portions) of fidyah to a single person?
Yes, it is permissible to give multiple mudd of fidyah to a single person, because each day of fasting is considered an independent act of worship.
Does the clipping of nails nullify ablution?
No, it does not, and it is preferable to wash the hands afterwards.
Does swallowing a fly, road dust, or flour dust break the fast?
A fasting person does not break their fast if something enters their body cavity against their will, such as a fly, road dust, or flour dust.
Is the marriage contract considered valid if concluded at home by the marriage official (Ma`zon)?
Yes, it is valid as long as it is registered at the court.