Lot you are covering here but quick fire.

1. No it is not correct. Sex is a multifaceted thing split between chromosomal, phenotypic and hormonal aspects. Horomonal transition changes phenotypic (physical structural aspects of sex) structures and changes the way the body chemically responds to fit a physical presentation more in line with the group the person is transitioning to more than the group they transition from. If you wanted to be very pedantic about it in a way that is somewhat unkind post medical transition trans people are functionally intersex but for medical purposes like determining dosages of medications and how they respond to medical procedures they are consistent with membership of their post transition group. A trans woman treated as a man by a pharmacologist would be getting the wrong dosage. In this case they need to be medically treated as a woman to receive adequate care.

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2. The assumption that there is inherent biological factors that do not change create logistical problems and errors in medical care. There is a widespread lack in the medical system of doctors who understand these principles which mean trans people can receive varying quality of care from people like EMTs or Emergency services based on the political whims of the place they are in. It also throws gasoline on bigoted rhetoric that trans people aren't "real" but are frauds "just pretending" as though their needs to be treated as their sex are just skin deep and not a complex mix of complex and fundamental biologic changes and a series of mental and social challenges of interfacing with a society that is unprepared to do the work to understand these differences.

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3. Calling a trans woman "biologically male" is just calling her a man under a different format. That's really all it is. It affects a trans person mentally the same because it causes them to have their physical characteristics reported back to them the exact same way. It tells them "we don't care about your psychological needs" The term "biological" being used isn't scientifically consistent with what is actually going on. The terms are "trans" and "cis" women/men because that registers the difference of experience in a way that doesn't take one's greatest challenges of existing and shove their nose in it. It acknowledges that they have crossed a boundary and are what they say they are. "Biological male" is bigotry disguised behind a pseudo scientific veneer.

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4. It contradicts. "Biologically male" places the EMPHASIS on MALE. When looking at any gender inclusive or gendered language the noun is key, the adjective is supplement. A femBOY is a man who is comfortable in his manhood with the gender expression that is feminine. A tomGIRL is the opposite. A trans WOMAN and a cis WOMAN are both in language affirmed as culturally feminine. A "Biological MALE" is medicalizing that persons experience and placing the emphasis not on their cultural experience or on their psychological needs, it's fronting the speakers desire to comment on that person's body and categorize the subject as a man with a masculine experience.