Option #2: No, her sample is not an appropriate, random sample. It does not represent the whole population.
The reason for this is that the student is only testing ice samples from coffee drinks at her local coffee shop. This specific context may not provide a representative sample of ice cleanliness from all coffee shops or beverage establishments, or even from the same coffee shop across different times of day or different days. A more comprehensive approach would involve sampling ice from various locations and times to better assess the overall cleanliness of ice in her community or the broader population.