Free will of every human being is a Quranic fact which can never be denied, Every human being is free to be a believer or a disbeliever, then all will meet the results of their own deeds and decisions. In Quran (We Have Guided him to the right way, then he decides whether to be a grateful or ungrateful. Sura 76, Verse 3.

The Knowledge of Allah (SWT) is unlimited and He Knows who will do what and when and where, but it never means forcing people to do wrong. Those who do wrong do it by their own decision and free will same those who do good. Allah (SWT) Helps doing good and never Helps doing bad.

Wassalam.

When tap water is used and the Najis item (A'yn al-Najasah) is removed then there is no question of impurity remains. Cat food by itself is not necessarily Najis unless it contains Najis ingradeint.

Wassalam.

Practicing sports and physical exercise which help our body and health is recommended as the Hadeeth states: Surely, your body has right on you إنَّ لِجَسَدِكَ  عليكَ حقّاً. Biharul Anwaar V.70, page 128.

Also (Surely, Allah Likes the strong person)إنَّ اللهَ يُحِبُّ الرجلَ القويّ. Biharul Anwaar , V.64, page  184.

Wassalam.

Zainab was one of the three fostered daughters of the Prophet Muhammad (SAWA) and Khadeejah (AS). Many scholars say that the only biological daughter of the Prophet was Fatima (AS). Zainab had a daughter called Umamah bunt Abi Al-A'aas or bint Al-A'aas. Umamah was married to Imam Ali (AS) after the martyrdom of Lady Fatima (AS) and according to Lady Fatima's will. It is mentioned that Umamah has a son called Muhammad Al-Awsat son if Imam Ali (AS) who was martyred in Karbala.

Wassalam

Yes it permissible to perform Ghusl while taking a shower using soap and shampoo. You need to have the intention of performing Ghusl for the sake of Allah, then making water reach to your head and neck, then the right side of your body then the left side of your body.

Wassalam.

Your Ghusl is valid because small hair fragments do not prevent water from reaching to your body.

Wassalam.

The fact that Ali is the best of human beings (Khairul Bashar) means the best of all human beings after the Prophet Muhammad (SAWA) and it never means that Ali is better than the Prophet Muhammad at all. This Hadeeth has been narrated many well known Sunni books like:

1. Musnad Ahmed Bin Hanbal, Fadha;I'll al-Sahabah, Hadeeth number 917 and 1110 and 177. 
2. Mussannaf Ibn Abi Shaibah مُصَنَّف ابن أبي شيبة  number 31503.

3. Kanzul Ummal, V.11, page 625.

4. Ibn Asaakir in Tareekh Dimishq , V. 24, page 372.

5. Al-Qandoozi Al-Hanafi in Yanaabee'ul Mawaddah , V.2, page 78.

Ali (AS) is the best of the Ummah of the Proohet Muhammad (SAWA).

Wassalam.

The Prayer is still valid as far your intention to continue praying for the sake of Allah  is not terminated or stopped or changed. Distraction during the prayer is from Shaitan who always tries to disturb us and spoil our relationship with Allah. It does not invalidate the prayer but you need to focus again on the prayer and avoid the Satanic thoughts (whispering).

Wassalam.

Investing in any company which has lawful activities and lawful income is allowed. Getting some interest from non Muslim banks is allowed according to many leading scholars as far as it was not under demand of RIBA (Usury).

Wassalam.

Virgin girl does require in her marriage the permission of her father or her paternal grand father. If father and the paternal grand father refuse proposal of marriage with out valid Islamic reason when the proposal is from a Kof’ (Compatible believer) and the girl needs to marry to save herself from sin, then the condition of the father’s permission or paternal grand father’s permission will not remain. That is when the refusal of the father or his father is not based on a valid Islamic rules.

Wassalam.

It is better to keep your issues with your husband between you and him with out involving others as much as possible. If you both are completely unable to sort your things together then a person from your family with a person from his family can be involved to sort things out. Don't try to make your parents take a negative opinion about your husband by hearing your side of the story before hearing his side. Involving your parents should repair and strengthen the relation between you and your husband and never to create enmity or bad feeling between them and your husband. You and your husband should talk peacefully to understand the reasons of your misunderstands and to try to avoid it as much as possible.

Wassalam.