When are placemats needed when eating, and why are they needed?
Off the cuff:
Placemats are used to make someone cognizant of something at the table he should not partake of. On a strict halachic basis, it would allow a person to
Eat with someone who is eating a food of an opposite milk/meat type (not necessary for kosher/treif as we aren't concerned for sharing)
Eat with one's wife at the table when she is a niddah
Additionally, there is a custom to not eat dairy on a meat table and vice versa, even if the table is clean. A placemat would help for this. It is not necessary for a non-kosher table.