Is it permissible for a woman to apply Kuhul (Halal eyeliner) and go out wearing it?
Kuhul is part of a woman`s adornment, and it is forbidden for her to show that to anyone other than a husband, or a Mahram (Unmarriageable kin).
Is Iddah (waiting period) incumbent on an old lady whose husband had died?
Upon the death of the husband, Iddah is incumbent on the wife regardless of her age.
Is it permissible to make up for missed fast after the beginning of the second half of the month of Sha`ban(the month before Ramadhaan) ?
Yes, it is permissible, but one who had missed fasts should hasten to make up for them. As for the Hadith mentioned in this regard, the prohibition is for offering absolute voluntary fasting.
What is the ruling on staring at the Holy Ka'abah?
All perfecy 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 family and companions.
Staring/looking at the Holy Ka'abah is an act of worship even if this took place while performing a prayer, since Al-Baihaqee stated that the Prophet (PBUH) said: " Staring at the Holy Ka'abah is an act of devotion." [Sho'aab Al-Imaan]. And Allah Knows Best.