Clary was quite popular in Sweden in the first half of the 20th century. I was surprised it's not in the database. It's a form of
Clara, I guess. Swedish 19th century queen
Desideria was born
Désirée Clary - in her case it was a surname, but it might still have inspired the use of it as a first name.
I'm not sure if Elice is intended as an alternative spelling of
Elise or as a form of
Elicia, they're both currently in vogue. (I'm not sure quite was
Elicia is either, though ... Just a twist on the popular
Felicia and
Alicia?) I would definitely think it's pronounced like
Elise (e-LEES), in any case.
Ida and
Kerstin are indeed both
Astrid Lindgren characters, but it's more a case of those characters having common names than this child having a very
Astrid Lindgren-y name. :) Or well,
Ida was revived due to
Astrid's
Ida, of course, but that was 40+ years ago so now it's just a common name.