What is the ruling on seminal fluid (mani) being discharged merely by speaking with a girl on Facebook and over the phone, when the conversation is devoid of arousal, and is ghusl (ritual bath) required every time, and does this invalidate the fast during the day in Ramadan?

You must fear Allah and stop speaking with that woman, as this is among the footsteps of Satan which lead to disobedience. Allah Almighty says: "O you who have believed, do not follow the footsteps of Satan. And whoever follows the footsteps of Satan - indeed, he enjoins immorality and wrongdoing." Speaking with a non-mahram (definition) woman without need is a cause for temptation and is forbidden.

As for what is discharged from you, it appears to be madhiy (pre-ejaculatory fluid) and not maniy (semen). Madhiy is a clear, sticky fluid that is discharged when thinking about lustful matters. Its ruling is similar to urine in terms of impurity and the obligation to purify oneself from it. It does not necessitate ghusl (definition) (ritual bath), nor does its discharge invalidate the fast according to the prevalent opinion. If we were to assume it was maniy, then your fast would be invalidated, and you would be obligated to refrain from eating and drinking for the rest of the day and make up for that day later.