Does bleeding from the body, such as from wounds, invalidate ablution?
Bleeding doesn't invalidate person's ablution. And Allah Knows Best.
Is it permissible to swear by (Allah "The Living")?
Yes, it is permissible because "The Living" is one of Allah`s Attributes.
Is photography forbidden, such as photographs of children?
All perfect praise be to Allah the Lord of the Worlds. May Allah`s peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
If there is a need for taking photographs of children or adults, then this is allowed. However, taking photographs of women shouldn`t be tolerated. Rather, they must be taken while wearing Hijab and must be kept in safe hands. And Allah The Almighty Knows Best.
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.