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No. Allah’s name is not for decorative purposes!

Syeds are the descendants of Prophet salla Allahu aliaihi wa sallam. But not all those who claim are actually his descendants. Even if they were, the only thing that makes a person honorable is his piety and good deeds not his ancestory.

Nothing prescribed, you can make Duaa in general, seeking times of accepting Duaa.

If you intend to buy the products just to win the money is haram, but if you are going to buy the product in any way whether there is a gift or not , the money in this case is halal.

You must be patient and satisfied with Allah’s Will and Decree and keep on making dua. Kindly refer to the following link(s): Dua to get a child | By Assim Al Hakeem https://www.youtube.com/watch?v=irMcAy7uuNY

You must give it to the person you took it from. If you don’t know him, give it in charity.

No problem in shopping and buying halal products.

This is cheating and is not permissible. If you must study these subjects, study to pass the exams without believing in it.

If you do your best to lower your gaze and don’t intend to gaze in sha Allah, you are not sinful.

You can change your first name but it is not obligatory unless it holds haram meaning. You must not be called after anyone except your father’s name and your family name.