Upon her confession early in the episode, Rebecca Morley is arrested by DI Neville Parker. But he doesn't caution her or inform her of her rights. Neville continues to ask Rebecca questions, which she answers without being given access to legal advice.
There is no "lethal dose" of arsenic, nor a set time in which it would become fatal.
Inhalation of arsenic gas is usually lethal in less than 30 minutes, but no-one even suspected gas had been used. It is actually possible to ingest high levels of arsenic for years without it being fatal.
Medical sources give the amount of arsenic that is usually fatal as anything between 100mg and 1400mg, such a wide range cannot be called a "dose".