What is the ruling on using the phone to search for a fatwa when one forgets the final Tashahhud in prayer, what is the criterion for the duration of the separation, and is it permissible to speak with someone during it?

If a worshipper remembers after concluding the prayer that he omitted a pillar, he should perform it and then prostrate for forgetfulness (sujud al-sahw), provided the interval was not prolonged or interrupted by an ablution-breaking event. Otherwise, he must repeat the entire prayer. The determination of a "prolonged interval" is based on custom and common practice, measured against the Prophet's (peace be upon him) situation in the Hadith of Dhu al-Yadain.

Using a phone to search for a fatwa during prayer is considered an action not belonging to the prayer itself. If this action is extensive, it may invalidate the prayer. However, if it is minor, there is no harm. The distinction between minor and extensive action is determined by custom, or by actions similar to those of the Prophet (peace be upon him), such as carrying Umamah or opening a door. If the action is extensive but for the benefit of the prayer, the prayer is not invalidated, such as shifting the qiblah.

As for speaking during prayer, if it is intentional, not for the benefit of the prayer, and with knowledge of its prohibition, it invalidates the prayer by scholarly consensus. However, if the speech is for the benefit of the prayer, the preponderant opinion is that it does not invalidate it, as in the Hadith of Dhu al-Yadain. If a worshipper asks someone else about how to act when forgetting the tashahhud, it appears that his prayer is not invalidated because it is speech for the benefit of the prayer, though it is preferable to restart the prayer to avoid scholarly disagreement.