Is prayer nullified by having thoughts while performing it?

Prayer isn`t nullified by having thoughts while performing it, provided that the praying person offers all of its pillars and meets all of its conditions. However, the reward decreases significantly in the absence of reverence since a praying person is rewarded according to the attentiveness of his/her heart during prayer.

What is the ruling when the monthly period when exceeding (15) days?

The maximum duration of menstruation is 15 days. If it exceeds this, it is considered irregular bleeding (Istihada). In this case, one must perform ghusl (Ritual bath) after menstruation, pray, and make wudu for each prayer after its time begins. She should return to her previous menstrual habit regarding duration and timing. For example, if her period used to be from the 20th to the 27th of each month, this is considered her menstruation period. Anything before or after this is Istihada, during which she only leaves prayer and fasting for the habitual menstrual days, then performs ghusl and resumes praying.

Does offering Udhiyah (Offering a Sacrificial animal at Aid Al-Adha) avails from offering Aqiqa?

Offering an Udhiyah doesn't avail a person from offering Aqiqa because each of which is a different act of worship. And Allah Knows Best.

What is the ruling on someone who prays Fajr late, after sunrise, knowing that they wake up on time but return to sleep and do not perform it within its time?