1a] She ran away from her family’s home and marrieda Christian; is she entitled to a share of her father’s estate?

1a]
It should be noted that one of the things that invalidate one's being
a Muslim and that constitutes apostasy is not regarding as
disbelievers the People of the Book and the mushrikeen, or having some
doubt as to whether they are disbelievers, or regarding their religion
as valid. See the answer to question no. 31807 and 6688
What you have to do is advise your sister and explain the seriousness
of what she has said, and call her to leave her husband ifhe does not
become Muslim.
To sum up the issue of her inheritance: if she remained Muslim and did
not regard as permissible her marriage that she knew was invalid, and
she did not regard the religion of the Christians as valid ordoubt
that they are disbelievers, then she may inherit. Otherwise if she has
done any of these things that invalidate her being a Muslim, then you
have to advise her and askher to repent in front of scholars in your
country. If she repents, all well and good, otherwise she is an
apostate and has no right to inherit from your father.
And Allah knows best.