Not sure how best to sort this out (there are other on these boards who are far more experienced than I!). Try posting this message in the Lufthansa forum, where you will likely get more help.

Don't worry about the NG flight posting as OS - all NG flights have OS flight numbers, and if the flight number is OS3XXX, then it will count as NG. Flights will never appear on the statement as "NG", but the computer will recognise them from the flight number.

That leaves you with 4 airlines that have posted (LH, OS, NG (with OS number), SK). For the TG sectors that have not posted, send or fax the original boarding cards and the ticket receipt to Miles and More in Germany (your local LH office will have the number), making clear you are taking part in the 55555 promotion and which airlines you believe the flights should post to.

For your wife, the local Miles and More office in Spain should be able to send you a printout, even for a temporary card.

Hope this helps!