Is it permissible to swear by (Allah ”The Living”)?
Yes, it is permissible because “ The Living “ is one of Allah`s Attributes.
Is it permissible to delay menses by using medication in order to fast Ramadhaan?
It is permissible for a woman to use medication in order to delay her menses so that it becomes lawful for her to fast Ramadhaan, but it is better that she doesn`t do so, and taking the medication is prohibited if she, or her doctors know that it involves a risk on her health.
Is a woman`s nephew by suckling considered a Mahram( i.e. unmarriageable)who is permitted to accompany her to Hajj?
All that is prohibited by lineage is prohibited by suckling, and a nephew by suckling is a Mahram like a nephew by lineage ;therefore, it is permissible for him to be a Mahram for his aunt in Hajj and Umrah.
Zakah due on a woman`s jewelry?
Zakah(obligatory charity) isn`t due on a woman`s jewelry used for ornament, provided that the value of each peace is within the range common amongst people.