You are hearing the "s" in the normal speed version because the following word begins with a vowel (not because it is plural) - see the info under liasons here: https://www.duolingo.com/skill/fr/Common-Phrases/tips-and-notes.
In exercises where there is a liaison like this, although you hear the "s" in the normal speed version you won't hear it in the slow version as each word is being pronounced individually.
Rely on meaningful/logical Duolingo sentences? At times they only look for grammatically consistent constructs. Many times the correct answer would seem obtuse to native speakers (and they say so in the comments). From time to time they look for meaning. it is just a toss up.
well there was the old woman who lived in the shoe and she had a bunch of kids- maybe it was blue and the girls all loved their blue shoe. duo has plenty of other wacky sentences, why not they love their blue shoe???? Duo usually does accept the singular and plural in the type what you hear sentences where there is no audible difference between the two.
Possessives change to match the noun that is possessed (for both gender and number) so in the same way that you would say "ma chaussure" for "my shoe" and "mes chaussures" for my shoes, you would say "Elles adorent leur chaussure bleue" for "they love their blue shoe" or if it is more than one shoe "Elles adorent leurs chaussures bleues" for "they love their blue shoes". Leur = their for a singular noun and leurs = their for a plural noun. The duo Tips and Notes on Possessives has more details here: https://www.duolingo.com/skill/fr/Possessives-1/tips-and-notes.
It can often be hard to tell whether something is singular or plural unless you have context. In this case you could make an educated guess as they are more likely to be loving their shoes than their shoe. You also know that it is "elles adorent" and not "elle adore" because there is a liaison and the "s" at the end of "elles" is pronounced because "adorent" starts with a vowel sound (see: https://www.duolingo.com/skill/fr/Common-Phrases/tips-and-notes for info on liaisons).
In French the indefinite article can be used to mean 'one each', such as
Ils ont un manteau — They have one coat / They each have one coat (from https://www.duolingo.com/skill/fr/Verbs%3A-Present-1/tips-and-notes)
Does this not apply to possessive adjectives?