Is it permissible for a woman who broke fasting due to a delivery to pay a ransom?
She should make up for the missed fasting days once she becomes ritually pure, but it is impermissible for her to pay a ransom while being able to fast.
Is it Permissible to lighten the eyebrows (I.e. Dye them blond)?
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, sallallahu ‘alayhi wa sallam, is His slave and Messenger.
Lightening the eyebrows is applying dye to them, and it is permissible to dye hair with other than black. The proof of this is the Hadith related by Muslim on the authority of Jabir told that when Abu Quhafa (Abu Bakr’s father) was brought on the day of the Conquest of Mecca with his head and beard white like hyssop, the Prophet (PBUH) said: "Change this with something, but avoid black."
However, it isn`t permissible for a Muslim woman to show her ornament (Zeenah) in the presence of non-Mahram men (Men permissible for a woman to marry). And Allah The Almighty Knows Best.
What is the Time for Making up Fajr Prayer and Other Missed Ones?
All perfect praise be to Allah The Lord of The Worlds and may His Peace and Blessings be upon our Prophet Muhammad and upon all of his familty and companion.
The Messenger of Allah (PBUH) said: "Whoever forgets a prayer, let him perform it when he remembers it." [Muslim]. As soon as you (Questioner) wake up, you are obliged to make up the missed Fajr prayer. And Allah Knows Best.
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.