Is the aforementioned girl required to observe an 'iddah period if divorced before consummation, and is she considered Islamically betrothed to the one who proposed to her and was accepted, and what are the Islamic implications of that?

If a woman is divorced after consummation (Dukhool) or valid seclusion (Khalwa Sahihah), she must observe the Iddah (waiting period). It is forbidden to explicitly propose to her or marry her during this period. What transpired between you two is not considered a valid Shariah marriage. You both must repent to Allah and sever the relationship. If her Iddah period expires, then a valid Shariah marriage can take place with a guardian (wali) and two witnesses.