I am an aromantic and an asexual man, meaning that I am not attracted to any gender in any way, so I was wondering if it would be halal for me to talk with a woman, just as a friend, nothing more? Is this also haram for me? Is it a punishment from Allaah (to be aromatic and asexual)?

All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger. 

The fact that you are not attracted towards women and are not sexually aroused towards them does not necessary mean that this is a punishment from Allah; rather, this may be just a test because this life is a test. Allah says (what means): {And We test you with evil and with good as trial; and to Us you will be returned.} [Quran 21:35]

Therefore, you should be patient and seek the means for treatment, such as supplicating Allah and consulting specialists, especially psychiatrists.

Being as such does not justify befriending a woman or speaking to her without a need, because it is forbidden in Islam to take girlfriends; as Allah says (what means): {…desiring chastity, not unlawful sexual intercourse or taking [secret] lovers.} [Quran 5:5]

The verse is general and it does not address only a certain category of people. If you will not be tempted by her, she might be tempted by you. Also, mixing with her may arouse your desires towards her and you end up committing a sin. For more benefit, please refer to fatwa 260941.

We ask Allah to spare us and you every evil and affliction.

Allah knows best.