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 Fatwa that you referred to states that a Muslim woman should not take non-Muslim females as close friends with the true meaning of friendship, and this is not specific to the time of war.
Indeed, the Sharee’ah forbade befriending and keeping company with dissolute Muslims, let alone with non-Muslims.
What is mentioned here about a Muslim woman also applies to a Muslim man; this is a general rule for men and women.
In any case, there is nothing in that Fatwa or the verse that you referred to, which prevents speaking with non-Muslims, or dealing with them in all that is permissible. The Prophet used to deal with non-Muslims in money and other matters.
‘Aa'ishah said: “The Prophet died while his shield was mortgaged with a Jew in return for thirty Saa' of barley.” [Al-Bukhari]
Allah knows best.