Matthew does that, for legal purposes, just as we would take the surname of an adopted father.
Sure - genealogies may use either biological (obviously the strict sense) or legal parentage.
We wouldn't write a genealogy using an adopted parent's ancestry, though.
Yes you would, certainly in the Jewish context where there are many examples of either biological or legal parentage being used - indeed you've tried to explain away Salathiel and Zorobabel.
So since there was only one natural parent,
That is clearly not true, but nonetheless ...
Luke would have used her genealogy.
You may wish that to be true to get yourself our of a 'belief before evidence' hole, but there is no evidence for this - Luke is clearly talking about Joseph and Joseph's father as he starts his genealogy. Were he using her genealogy and did not want to mention women (why?, others do) then he'd simply skip a generation from Jesus directly to Mary's father - there would be no earthly point in even mentioning Joseph. Yet he does and is clear that Heli is Joseph's father, and onward from there.
I've noted your point about not believing other sacred and ancient texts. For another thread, maybe?
Nope, for this thread as it is an important issue - you are special pleading, cherry picking, bending arguments way beyond any evidence in order to prove your preformed belief to be true. Why is that the case and why not apply the same to other sacred texts. The point is that you aren't neutral in this discussion - you have a clear bias and you are only interested in 'evidence' as a means to justify your bias. That isn't objective - Jeremy and I are being objective - looking at the evidence (there is precious little of it) an applying a rational and objective approach to it, just as we'd do to other sacred texts.
And if you take an objective and rational viewpoint the following become clear:
1. There is no realistic way that people living in 1stC palestine would have been able to accurately trace back their ancestry over dozens and dozens of generations.
2. Matthew and Luke both include genealogies, and do so for a purpose and with an agenda, which is slightly different in each case.
3. Matthew and Luke are not in agreement - not unreasonable as neither would have access to credible information to substantiate their claims (see 1 above).
4. Their choices (and disagreements) likely reflect both inconsistent evidence available to them and the need to come up with the 'right answer' because of their agendas (see 2 above)
5. There is no evidence whatsoever to support the notion that either of them is describing Mary's lineage, rather than Joseph's.
6. Due to the inconsistencies Matthew and Luke cannot both be right, however they could both be wrong.
7. Trying to trace back to Adam is based on the myth that Adam was the first man - we know that not to be true and therefore the whole approach is flawed.