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Following week
No, this needs to be worded differently. Since Friday before Monday of the following week is the same as Friday of this week, one could say, "Send in your reports this Friday" or "Send in your reports Friday of this week." If the intent is to mean Friday of next week, and not the current week, one could say, "Send in your reports Friday of next week. Using a date as well as the day of the week would make it clearest: "Send in your reports Friday, December 17." It is interesting to note that even native speakers of English are often confused about what "this Friday" or "next Friday" mean, so it is best to supply enough information that the intended Friday is absolutely clear.
They mean the upcoming week.
the week after the current week
On a Friday, it is Friday and it is the 6th day of the week.
No. It would be better to say: every week on Friday the Friday of every week the week beginning every Friday
Most companies post them on Thursday, Friday or Saturday for the following week.
December 25th, 1952 fell on a Thursday. The following year it was on a Friday.
It means that it will be paid at then end of a pay period, rather than in advance. For instance if you are paid every Friday, then in arrears means that your pay this Friday was for the work week prior rather than the work week coming.
I interpret that to mean any day of the following week.
November 28th, 1951 fell on a Wednesday. The following year, it fell on a Friday.
April 16th, 2003 fell on a Wednesday. The following year it fell on a Friday.