Artificial insemination for a single woman

These are Christian values
Conservatism
Maybe beautiful, maybe less so
But what does that have to do with Judaism?

Which sperm is better, Jewish or Gentile?
With the sperm of a Jew, there is a concern about halakhic problems if the father is unknown.
With the sperm of a Gentile, there are methods that make the child doubtless Jewish (cited, for example, in the Tosafot rulings on Yevamot, but I have seen other poskim)
Perhaps the most optimal is shared parenting with a Jew or the sperm of a soldier who fell in battle.

In my opinion, the seed of a Gentile is better. Except for all sorts of mysticism, there is no problem with that.

Also for the methods that Wald is doubtlessly Jewish?

Strange methods. I wouldn't be afraid of them.

By the way, I don't know of such a method. In any case, there's no need to fear it.

Y.D., is the child probably Jewish or is the donor probably Jewish? After all, the child follows in the footsteps of its mother.
By the way, from what I understand, the Jewish donation also makes the child kosher.
(Regarding sibling marriages, if there is any doubt, it is always possible to rule out kinship through DNA testing.)

Yehudit, it is about the birth. There is a discussion of this opinion in Pithei Teshuva Even HaEzer, Section 4, Subsection A:
https://www.sefaria.org.il/Pitchei_Teshuva_on_Shulchan_Arukh%2C_Even_HaEzer.4.1?lang=en

And on the Otzar Hochma forum:
https://forum.otzar.org/viewtopic.php?t=51558