Learn Italian: Ha sottovalutato il problema, ma non se ne è accorta. - She underestimated the problem, but she did not realize it.

The infinitive is accorgersene (to realize it / notice it). It combines the reflexive verb accorgersi (to realize) and the pronoun ne (of/about it). Remember that when the reflexive pronoun si is followed by ne, it changes to se.

What exactly does ne replace in this sentence?

It replaces the concept of del problema (of the problem). The verb accorgersi requires the preposition di before an object (accorgersi di qualcosa). To say she didn't realize "it", we must use ne to replace that entire di phrase.

Why do we use the auxiliary essere (è) for the second verb but avere (ha) for the first?

The first verb, sottovalutare (to underestimate), takes avere like most standard verbs. The second verb, accorgersene, is built on a reflexive verb. All reflexive and pronominal verbs require the auxiliary essere in compound tenses.

Why does the past participle accorta end in -a? Does it agree with ne?