I am not familiar with Cairo’s current procedures, but I would not leap to the assumption that this is something to be concerned or panicked about right now.
When there is an officer review of the details/documentation of a non-immigrant visa case (which a K-1 technically is) prior to the interview, the officer usually either issues the visa or sends an interim refusal until the interview. The interim refusal may suggest additional information to bring to the interview. For example, if someone has applied for a visa under the Interview Waiver program and the officer decides that the person really needs to be interviewed, they will issue a 221(g) refusal and require the person to come in for an interview. They will tell the applicant if there’s a specific piece of information to bring with them.
It appears to me that what Cairo is doing is reviewing the case for completion prior to the interview, to help applicants come fully prepared with everything they need to bring. To document the review and what was requested, they issue the 221(g) sheet. Since none of the main areas were checked on the OP’s sheet as far as I could see, it seems to me that they were likely satisfied with the basic documents, but wanted to indicate that documentation of a solid, bonafide relationship is very important — probably THE most important part of the application..
NOTE: If someone has gone through Cairo for a K-1 visa recently and my basic assumption about their process is wrong, please let me know and I’ll reassess this response!
About asking for an earlier interview — the date you received is likely the earliest open date. Unless you have a valid reason (other than, of course, wanting to be together as soon as possible), it is unlikely that you will get an earlier date.