How do astrologers writes a Horoscope of new born child? Can they be accurate in determining one's life partner or destiny?
The astrological charts of a new-born baby are written taking the moment when the child takes its first breath (independent of its mother). The planetary positions at that moment determine the pre-destined portion of the child's life (prarabdha Karma that the child brings from its previous incarnations/births). Hence, the Natal horoscope (Jataka) will greatly shape the proceedings of the individual's course of life and will play a predominant role in influencing its will, determining the circumstances that the he/she will face and conditioning the abilities at different ages.
Having said that, the individual can use its free will to counteract the influences and, by virtue of blessing from higher souls, the individual can endure (and in certain occasions, overcome) the pre-destined fate.
Answering your second question, there is a curse on astrology that no human can have a accurate (100%) prediction on all aspects such as what, why, how, where, when and by whom (at the same time). However, with reasonable accuracy and precision, destiny can be deciphered (with decently accurately but limited precision). Life partner being a subset of destiny can also be predicted. Most predictions will be indicative and significantly reliable given that the astrologer is well learnt, the dashas and antardashas of the astrologer is reasonably favorable, has yogas that made him an astrologer with Vak Siddhi (capable of saying things that come true) and the querist has the bhagya to know the truth at that juncture of time.
Though all this looks complex by analysis, it is an experiential learning that will help have a better understanding.