The record as in The school record, There is a record of his reservation, or A phonograph record?
“The record” in the information sense, so either of your first two examples.
The "f" sound here is interesting/confusing. At least to my hear, it sounds like it's almost shading into a "th". Sometimes I hear it, sometimes I don't.
I definitely hear a slender 'f' here although to my Russian ears the 'slenderness' is quite weak.