No, she does not need to redo her prayers. Ghusl itself is not obligatory if she was not sure that she had the real climax discharge while she was asleep. Only remembering the dream does not mean that she had the climax discharge. 
'Wassalam.

Yes it is permissible any form of Salawaat during Salah.

Wassalam.

Applying medication for medical necessity is allowed as much as it is really necessary but it should not look like beautification at all. Muslim woman is not allowed to expose he beauty in front of the outsiders.

Wassalam.

1. Repeating Salawaat and repeating Estighfaar as many times as possible.

2. Giving Sadaqa.

3. Reciting Ziyarat Aashura.

4. Praying the Night Prayer (Namaz e Shab or Salatul Layl).

5. Praying for other believers.

6. Seeking the Waseela of Imam Al-Mahdi (AS) as he is the living Imam of our time.

7. Sincerely supplicating and seeking from Allah as He Said in Quran: Seek from Me, I will Respond to you (Sura Ghaafir, verse 60).

Wassalam.

After removing the Najis substance, pour little water on the Najis surface then wipe it, then again pour little water on it then wipe it. It becomes Taahir.

Wassalam.

Allah is always Intending everything done by everyone. The Prophets like Yahya was killed, and all our Imams had suffered a lot. They are the real winners despite all their sufferings, torture and martyrdom. Our life is not limited to this world but it goes on for our long future after this life, where we will see the results of our deeds. Allah Has Said in Quran : We Will definitely support our messengers and the believers in this worldly life and on the day of resurrection. (Sura Ghaafir, verse 51).

Wassalam.

Allah Says in Quran : He (human being) never alter an word with out two angles write it. Sura Qaaf, verse 18.

We must avoid mentioning others in any mindless statement. We need then to seek forgiveness from them otherwise we might loose or good deeds to them or carry their bad deeds. We need to repeat Estighfaar and be careful before any word we alter.

Wassalam.

Muslim female is fully responsible to maintain her full Hijab wherever she goes. If your studying abroad does not disturb your religious duties then yes, but if there is a risk or possibility of harm on you, then avoid that.

Wassalam.

Allah only Has the full knowledge of every unseen الغيب and He Grants whomever He likes whatever He likes from the knowledge of the unseen. See Verse 26 and 27 in Sura al-Jinn ( Verse 26 and 27, Sura 72). Allah mentioned in Quran the Prophet Easa used to inform people about what they ate and what they hide in their houses.Sura 3, verse 49.

These are just few examples about knowledge of unseen granted by Allah to His sincere servants.

We should not mix between the Whole unseen which us only with Allah, and the granted unseen by Allah to His sincere servants.

Wassalam.

This question need a full book to answer it. These are few brief facts:

1. Every rule in Islam is based on the benefit of the human being whether we know that benefit or not as it is best known by Allah (SWT).

2. Allah, The Glorious Does not need anything but we need to worship Him properly to live a real human life with peace and success.

3. Worship in Islam is within the limits of our abilities and there is no obligatory worship more than our real ability.

4. More we worship Allah, more we get benefit and elevation and peace of mind.

5. The Prophet Muhammad (SAWA) and his holy Progeny Ahlul Bayt (AS) are the teachers who teach us and all the creatures the real worship of Allah.

I advise you to refer to the sermon of Lady Fatima (AS) in which you will see the wisdom and reasons behind the main worships in Islam.

Wassalam.

It is not allowed to do anything which helps committing sins. Betting is unlawful (Haraam) in Islam and any act which helps it is unlawful and the income from unlawful work is unlawful.

Providing service to betting apps is unlawful like providing service to alcohol companies or adultery etc.

Wassalam.

Obligatory Prayers must be performed within its timings and nothing can be more important than performing the obligatory prayers. You should not allow any action which contradicts or causes not performing any obligatory prayers. You should help your husband to perform every obligatory Prayer within its timings and never make any schedule which contradicts any obligatory prayers.

Wassalam.