Is it permissible to speak with a suitor in the presence of family during the waiting period (iddah)?

It is not permissible for anyone to explicitly propose marriage to a woman in her 'iddah (waiting period), whether the 'iddah is due to divorce, death, or annulment. The ruling on implicitly proposing marriage (ta'reedh) varies depending on the type of 'iddah: In the 'iddah of a revocable divorce, implicitly proposing marriage is not permissible at all, because the woman in that period is considered in the status of a wife. However, in the 'iddah of death or an irrevocable divorce, implicitly proposing marriage is permissible, but not explicitly.

As for a woman speaking with a non-mahram man, it is permissible out of necessity, provided there is no fear of temptation, no seclusion, and no softening of the speech.