If an original plastic part came with wording or date codes that are not on licensed reproduction parts, is there a way to transfer the information to the reproduction piece to make it more original? Can a mold be made of the wording and plastic poured in it somehow, then transferred to the new piece?

No, the part number, Pentastar, etc. have to be engraved into the mold so they are integrally cast with the part.

Yes. You can do a resin casting of your part and out comes the part with the number.
Also, you can do a casting of just the raised numbers or other info. That can be done by a process called foil casting.
There is also another process called photoetch that can be done as well.
This is all from techniques through model car building.