Just FYI- there are various posts about this topic on VJ as well as other forums. So there is a known issue regarding DHS verifications but unfortunately no official acknowledgement or ETA of a fix yet. People experiencing this issue are unable to get help from any of the agencies involved and those that can use the SAVE check are seeing updates on it as described above (case returned) which should mean the verification was complete - however SSA is saying its not reflecting such on their end...
You are a K applicant. This means you must get the SSN issued before the i94 expires. SSA requires you have at least 2 weeks left on the i94 for them to process it. You may run out of time before the issue is resolved- in which case you will have to wait for the EAD to get a SSN. When you fill out the 765 make sure you check the appropriate box saying you want a SSN issued so you can avoid having to deal with SSA again. That checkbox in itself is rather new but has been working w/o much issue for those that utilized it (when the system was working properly at least).
Be prepared to need to wait for the EAD. Try to send in your AOS package asap. For health insurance a SSN is not required although your insurance company may attempt to tell you otherwise. If you have issues with insurance search the forums as there are several posts discussing how to get the insurance company to add your spouse w/o a SSN. For a DL unfortunately most states require such so theres no way around that except to wait. If he has a foreign DL you can look into your states requirements for how long he may be able to use it (if he can use it at all). Banks also have varying requirements for what is needed to open or add someone to an account. Some banks are more immigrant friendly then others you can use google to help sort which banks near you may open an account for you guys. Almost all banks though require immigrants to present their IDs in person and can not open accounts online hence why you would need a bank with a local location. If you are going to attempt to open a bank account at a new bank or add him to your current bank you will want to attempt to do such while the i94 is active. As you probably know once the i94 is expired the alien is placed into a period of auth stay while the AOS is processing. That is not technically a valid status. Once the EAD is issued however the alien does have a valid status (EAD holder) for SSA, DMV, etc.
I really hope your case gets sorted and the SSN is issued before the i94 expires. If not dont let it discourage you. Remember to show a bonafide marriage you need to show comingling of finances- that does not mean "joint" or "equal". It means whatever you have you both use- use meaning contribute and take from. USCIS also understands when someone comes on the K that often they are unable to open accounts and can not work until the EAD is issued so they dont hold that against you or view the lack of immediately opening joint accounts as a negative. You also may be a couple that never has a joint account. Thats fine too. It can also be helpful to gather evidences needed for AOS and later ROC as you go rather then trying to go back and dig up old documents. We all think we have good memories until it comes time to remember stuff! So perhaps for now consider printing out your monthly statements and highlighting or notating on it purchases that were made from your sole account that reflect the funds are used for joint purchases or purchases related to his expenses.