Marriage

Bismihi ta'ala

This will depend on what type of divorce was conducted. If it is raj'i (revocable), and within her 'iddah period, then they are husband and wife again.

And Allah knows best

Bismihi ta'ala

Such a thing holds no significance or value. The second nikah will not nullify the first, and it is just meaningless to do so. These are unforetunately Western practicises of "renewing vows", and things like that, which a Muslim definitely does not need to do.

And Allah knows best

Bismihi ta'ala

This engagement period, between the nikah and the wedding (or rukhsati) is a limbo time, where you are not single anymore, but should not consummate the marriage. 

It is a time best used for getting to know each other. You will come to understand whether this is right decision, or not, and if any red flags, or something serious can be seen, calling things off before intimacy is by far better than after.

A very important point is the value of the zafaf night. The excitement of the wedding night, or zafaf night, is that the newlyweds become intimate for their first time, after waiting during their engagement, for this special night. 

They observe all the mustahab things to do, on this night, reciting the prayer and the duas, and the husband washing the feet of the bride, and everything else. 

It will be a memorable time for the husband and wife. 

Loyalty to parents is a very serious moral requirement both sides need to have. You do not want to violate this trust by doing that, knowing the parents from both sides expect you both to wait for that special night. Therefore, morally you both have an obligation to be patient and wait for the wedding night, to consummate the marriage. 

The strength of your commitment to each other is showing your high Akhlaqi standards to each other, and to your parents and parents-in-laws. 

Although you might consider it as "societal traditions", but it is a very good thing. Of course, couples should avoid long periods of waiting from nikah to rukhsati. It is not good at all to have long engagements. 

Let it be known that if one was to have sex during this time, it would technically be halal, and not considered as zina, but they have committed something morally wrong, unless their families both allow it, or in their specific culture, there is no zafaf/rukhsati, or such ceremonies.

And Allah knows best

Bismihi ta'ala

It does not matter what madhhab or ideology the girl's father may be, her family should absolutely be involved, and her father must give consent for the marriage to be valid. Unless, of course, she meets the requirement of "balighah/rashidah". 

And Allah knows best

Bismihi ta'ala

No, there is no issue at all with doing nikah contract outdoors, or in morning. 

The only time it is makruh is when the moon being in the zodiacal sign of Scorpio (qamar fi al-'aqrab), and when the moon is absent (end of lunar month/beginning of lunar month), which is called al-mihaq. 

And Allah knows best