The quotes given in Dr Killgrove's article includes just those parts of the tablets where the translation is reasonably certain. While these may convey the broad meaning (in this case that the letters were complaints against the copper merchant Ea-nasir), it can be confusing when the individual letters are looked at in detail.
Details about the tablet you have quoted from Dr Killgrove's article can be found in Ur Excavations Texts V: Letters and documents of the Old-Babylonian Period by Hugo Heinrich Figulla and William James Martin. The designation of the tablet generally cited (UET V 6) comes from its reference in this volume.
A more complete transcription & partial translation of tablet UET V 6 can be found on pp40-41 of Foreign trade in the old Babylonian period as revealed by texts from Southern Mesopotamia by W. F. Leemans (Brill, 1960). I have reproduced an image of the text below:
(Click to enlarge)
As you can see, there is still a great deal about the letter that remains unclear.
However, there is a discussion about Ea-Nasir's role as a copper trader later in the book (from p51) which addresses some of the questions that you raise.
"you have given the copper": to whom?
It seems that Ea-nasir had given the copper to his ummeanum.
Ummeanum is a term which is often translated as "investor". See for example Aubet, Maria Eugenia: Commerce and Colonization in the Ancient Near East, Cambridge University Press, 2013, p339).
"and give the silver and its profit to Nigga-Nanna.": Is this a directive? Or a lament?
The wording ("ku-babbar u nemelsu ana Nigga Nanna") suggests that this is a directive, and might be taken from their contract (see p52 of W. F. Leemans book cited above).
The individual Nigga-Nanna is named in a number of letters, but as Leemans observes, their role
"is not absolutely clear"
"most likely he was a middleman between the principal at Ur and Ea-nasir, travelling abroad"
"I have made you issue a tablet.": A tablet is a pledge? A promissory note? Who has given the tablet to whom? I read this as Ea-Nasir having given Arbituram a pledge. In exchange for what?
The "talbet" in this context would appear to be the contract between Arbituram and Ea-nasir.
"Why have you not given me the copper?": I thought the copper was already given? Is this a subsequent transaction? Why has the copper not been given?
No, the copper had not already been given, and it is not a subsequent transaction. It seems that the copper was given to Ea-nasir's ummeanum (see above), rather than to Arbituram or his agent (presumably the named individual, Nigga-Nanna).
There are quite a number of surviving tablets which contain letters concerning dealings with Ea-nasir. Dr Killgrove's article mentions extracts from some of them, which support her description of Ea-nasir as
"possibly the worst businessman of the second millennium BC".
Several letters relating to Ea-nasir are described in W. F. Leemans' book. Obviously, an academic volume allowed (and required) a more detailed description of the letters than would be possible in a popular magazine article.
One Complaint tablet to Ea-nasir is even the subject of a page on Wikipedia. Better images of this tablet (accession number 131236) can be found on the Collection online page from the British Museum.