What is the ruling on using perfumes when the presence of alcohol in them is unknown, given the prevalence of alcohol in most current perfumes, and is it obligatory to inquire about this?

The basic principle regarding perfumes is that they are permissible, provided they do not contain alcohol. There is no need to ask the seller or the giver about their alcohol content when in doubt. However, if there is a strong presumption that they contain alcohol, then one must avoid them, because a strong presumption takes the place of certainty.