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 it permissible to swear by (Allah ”The Living”)?
Yes, it is permissible because “ The Living “ is one of Allah`s Attributes.
Is a woman`s neck an Awrah(private part)?
It is an Awrah, and it is forbidden for her to reveal it before non-Mahrams(Marriageable men).
Should vowed fast be offered in consecutive days, or not?
Vowed fast should be offered in line with what was originally intended by the vow-maker, either consecutively, or not.