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.
Chatting with a non-Muslim woman or laughing with her is not forbidden, let alone for it to be an act that takes a person out of the fold of Islam. Indeed, we are advised in the Sharia to deal nicely with the disbelievers, as Allah says (what means): {Allah does not forbid you from those who do not fight you because of religion and do not expel you from your homes - from being righteous toward them and acting justly toward them. Indeed, Allah loves those who act justly.} [Quran 60:8]
As regards the woman whom you mentioned in the question, then in principle she is a Muslim as you stated that she fasts Ramadan but she does not pray. The scholars of Fiqh differed in opinion about the ruling on someone who does not pray out of negligence and laziness. Most of them are of the view that he is not ruled to be a disbeliever, contrary to the well-known view of Imaam Ahmad that says that such a person goes out of the fold of Islam.
There is no agreement on the issue among the scholars; nevertheless, someone who does not pray is in great danger. It is enough evil for him that the scholars differed about him on whether he is a Muslim or a non-Muslim. For more benefit, please refer to fatwas 85264and 84235.
Instead of thinking about you becoming a disbeliever by talking to her or her becoming a disbeliever by abandoning the prayer, you should think about how to influence her and how to save her so that you will get a great reward. The Prophet said, “I swear by Allah! If Allah guides one single man (to Islam) through you, it would be better for you than possessing the red camels (i.e. the most precious breed of camels).” [Al-Bukhari and Muslim]
Being kind to her, showing compassion towards her, and speaking to her in a gentle manner are among the major things that would help you influence her heart and make her respond to your words and your advice, in addition to supplicating Allah in her absence to guide her. The Prophet said, “The supplication of a Muslim for another Muslim brother in his absence is accepted by Allah, as he has an appointed angel at his head, and every time he supplicates for his brother to a good effect, the angel would say, 'Aameen and for you the same.'” [Muslim]
For more benefit, please refer to fatwas 12803 and 13288.
Allah knows best.