This teshuva encompasses several short teshuvot concerning different cases of גיורות.
In the first case, Rav Moshe Feinstein was asked about a woman who converted but did not keep the mitzvot initially as her husband was not so religious. However, her husband subsequently became more observant, and she followed suit, and now she was concerned whether her conversion might be invalid due to her failure to accept the mitzvot at the time of the conversion. Adding to the complication was that the couple had already had several children. Rav Moshe ruled that the woman should undergo a second conversion (i.e. טבילה) and the children should as well (although he did not require the sons to have הטפת דם ברית).
The second case dealt with was of a non-Jewish woman who married a Jewish man and was pregnant and then decided to convert. Due to her pregnancy, she was unable to travel to a place where there was a valid בית דין and she did not feel comfortable going to the mikveh in front of men. Thus, the question was raised whether three untrained men could serve as the בית דין and if women could observe her going to the mikveh. Rav Moshe ruled that her case did not rise to the level of שעת הדחק and that if she was not ready to accept the mitzvot in full - as evidenced by her reluctance to convert properly - then she should not be accepted as a גיורת. However, Rav Moshe notes that if she does convert, then she does not need to separate from her husband from three months, as she is already pregnant.