On the charge/accusation/allegation of

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A. The police arrested him on the accusation of drug dealing.

B. The police arrested him on the charge of drug dealing.

C. The police arrested him on the allegation of drug dealing.

Q1) Are sentences A,B,C all correct English? (I would say yes)

Q2) Do "on the accusation of", "on the charge of", "on the allegation of" modify the verb "arrested"?

(I would say yes because the police arrested him according to accusation/charge/allegation)

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D. On the accusation of drug dealing, the police arrested him

E. On the charge of drug dealing, the police arrested him

F. On the allegation of drug dealing, the police arrested him

Q3) Are sentences D,E,F all correct English as well, regardless of the placement of "on the accusation of", "on the charge of", "on the allegation of"? (I would say yes because the different placement doesn't affect them to modify another one)

Q4) What does "on" mean in "on the accusation of", "on the charge of", "on the allegation of"?

I think that "on" is used to mean "regarding" or "according to" the same way that "on" is used in sentences S1, S2, S3 below, but I would like to see what you would think of the meaning of "on", which is used in sentences A,B,C, comparing S1,S2,S3.

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S1. We purchased the computer on the understanding that it could be returned within ten days.

S2. We are operating on the assumption that the loan will be approved.

S3. She has made a series of documentaries on the subject of family relationships.

Q5) In S1, does "on the understanding" modify the verb "purchased"? (I would say yes)

Q6) In S2, does "on the assumption" modify the verb "are operating"? (I would say yes)

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G. The former director of Nike France is subject to investigations on the charge of falsification.

H. On the charge of falsification, the former director of Nike France is subject to investigation.

Q7) Are both sentences G and H correct English? (I would say yes)

Q8) What does "on the charge of falsification" modify in both sentences G and H? (I have no idea how to analyze it in this case)

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Thank you very much