Is it permissible to pause during the recitation of Al-Fatiha at Allah's saying: (You alone we worship and You alone we ask for help) to ask Allah for a need, and then resume the recitation?

It is not legislated to supplicate when reciting (You alone we worship and You alone we ask for help) in Al-Fatihah, because it was not reported from the Prophet (peace and blessings be upon him) or the Salaf. It is sunnah for the reciter, both in prayer and outside of it, to supplicate at verses of mercy, seek refuge at verses of punishment, and glorify at verses of glorification. The question intended in the noble hadith after the saying (and My servant shall have what he asked for) is the request for guidance to the straight path, as stated in His saying, the Almighty: (Guide us to the straight path).