Firstly three weeks isn't a lot for a complaint, particularly if escalated to the CEOs office. You might get a reply via that route, but it's usually best not to complicate complaints until you've received an unsatisfactory response.

Taking all the points one by one:

• Conformance is king at LHR. Even if your connected to flight leaves late it takes heaven and earth to get reinstated onto it, even if you have a lot of status. That complaint isn't getting anywhere I'm afraid. You should be booked onto a later flight, you were offered Newark but rejected it (fine). You asked for JFK and for seats together, which you got. I can't see a complaint being warranted here, you got the outcome you wanted.
• I would definitely claim for wifi, and I think you'll find BA accept this under the circumstances even though strictly speaking they're not required to. I'm glad you got sorted out for the transfer. Incidentally, the fixed fee taxi from JFK to manhattan (not quite $50 because of tolls and the ubiquitous tip) is quite a good option rather than booking a transfer.
• The accident/injury issue is serious, and I would absolutely be chasing that. There should at least have been a proper report form filled out, and if there wasn't it's quite serious. You should probably have seen a doctor and had an assessment done, but too late now. For me, this is the only real substantive complaint in the list. In fact I would have a separate complaint for this entirely.
• Broken suitcase is a standard issue, not really connected with any of the above, straightforward claims process, you may not get as much as you expect as it depends on the age of the suitcase and so on.
• It was your decision to buy better seats. I can understand why you did it, though another solution might have been for you to swap with her away from the aisle if she was worried about a bag falling down, It doesn't happen a lot. BA might be sympathetic under the circumstances but it's not all that likely.

I'd be fairly certain you won't get an upgrade; BA don't really do that. You might get a refund of the seat fees, you should get compensation for the suitcase, you will probably get a wifi refund, there's a good chance of a gesture of an e-voucher or avios for the various problems.. Beyond that, most of this is in the realm of "these things happen", and there's no causal link between them, the linkage is really about frustration with absolutely everything going wrong and you presumably having to comfort an upset companion during what was supposed to be a pleasant break.

As a general observation, complaints of this type need to be quite concisely expressed. You'll get a better, quicker, response if you stick to the absolutely essential facts, because complaints will be coming in thick and fast to agents, and if the issues are difficult to understand they'll tend to be pushed aside or given an unthinking response.