You may be able to find the info you want by requesting a copy of Anna Craig's original social security card application. Depending when she applied, the application may include her parents' names, and it should include her maiden name. There is an Anna Craig listed in the Social Security Death Index with the birthdate you indicated.

You can request this copy from the Social Security Administration (you can get more info from their website).

For the marriage info, it would probably help if you know the specific municipality where the marriage took place, since marriage records in Conn. aren't generally kept at the county level. I'm not sure that a marriage in 1933 would be considered public info yet, but you can check on this.