foreign currencies transactions-AP

Hello Friends,

Can we do the following accounting with foreign currencies transactions.

Foreign currency PO receipt at one FX rate whereas the invoice entry is at another FX rate.
 
Ex:  PO 32404056 receipt 4235 and invoice 1234- FX rate at receipt 1.251, FS rate at invoice entry 1.2565. 
                                Accounting is cost center 0000 when it should be 55000
 
Second scenario:    Japan ACM issue:  PO raised in USD at one rate and invoice entered in USD at another rate, ledger is in JPY
 
Ex:             PO 35103965 raised in USD at 14.5 and invoice 146436 eneterd at 14.0327
                                Accounting is cost center 0000 when it should be 5500
 
3'rd scenario     Japan ACM issue:  AP Invoice entered at one rate and payment entered at another rate