Is it permissible for a woman in her waiting period (Iddah) after her husband's death to leave her house and mix with non-Mahrams?

It is not permissible for a woman in her waiting period (Iddah) after the death of her husband to leave her house except for a necessity, such as for medical treatment, nor is she allowed to mix with non-Mahrams. A woman is not permitted to mix with anyone other than her husband or Mahrams, whether she is in her waiting period or not. However, there is no harm in accepting condolences from those who visit and responding to their inquiries about her well-being. And Allah Knows Best.

What is the best remedy for a person who experiences Waswasah (whispers of the devil) during Salah (prayer)?

Such a person should ignore the devil`s whispers, contemplate the Quranic chapters and verses that he/she recites, look directly at the place of Sujood (prostration), make supplication to Allah, and take refuge in Him from the cursed devil.

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.

Is it permissible for a person who has to make up for missed fasts to fast six days of Shawwal (the month directly after Ramadan) before making up for the missed fasts?

Yes, it is permissible for him/her to do so, but it is better that they make up for missed fasts first. And Allah Knows Best.