Is this woman considered lawfully married based on the described contract, and if the contract is void, does a divorce take effect and is she obligated to observe the waiting period ('iddah), or is there no marriage in the first place?

If your friend's marriage was conducted under the guardianship of her adult son, with two witnesses present, and with the utterance of the offer and acceptance, then it is a valid marriage. The written contract is not a condition for its validity, but rather for establishing rights. If the husband consummated the marriage or was in seclusion with his wife and then divorced her, he may take her back as long as she is within her 'iddah (waiting period), without the need for a new contract.