Am I permitted to perform more than one prayer within single ablution?
You are permitted to pray as many as you could within one ablution and to recite Quran so long as your ablution isn't nullified.
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).
Are phone conversations between the two sexes permissible if for consultation, and within the limits of good manners?
Such act is impermissible since it renders hearts corrupt, and could lead to forbidden attachment. Allah, The Almighty, says: “and follow not the footsteps of the devil. “{Al-Baqarah/68}.
Is it permissible for a woman to go out wearing bright colors?
Bright colors are part of a woman`s adornment, and it is impermissible for her to show it to people other than her husband, or one of her Mahrams(Unmarriageable kin).