Answer: 1) A woman is not obligated to hear kriyas haTorah and may daven during that time.
2) She should daven at home, because there is no obligation for her to daven with a minyan, but she certainly has the same responsibity to daven with kavana.
3) Yes she should skip parts of pesukei d'zimra, because while she is not obligated to daven Shmona Esrei with a minyan, it is more important to do so than to say all of pesukei d'zimra in order. However birkos krias shema should not be skipped.
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