As you say, two rather wide questions; to which the answers are 'quite a few' and 'yes'. As with folktales, a great many motifs recur in traditional songs throughout Europe and further afield without this necessarily meaning that the songs themselves are directly related, but many studies have been made; usually in relation to specific examples, so you will probably mostly get replies here relating to specific songs or song groups rather than the broad topic.

Child of course went into extensive detail on the subject in The English and Scottish Popular Ballads, and many of the discussions here that deal with 'Child' ballads refer to analogues found in other parts of Europe: quite a few are quoted in various languages, with or without translations into English. 'The Outlandish Knight' ('Le Tueur de Femmes') and 'The Cruel Sister' come to mind among others; from the 'non-Child' canon, I recall posting French relatives of 'The Ship in Distress', for example: Penguin: The Ship In Distress. A Danish antecedent found by Child's mentor Svend Grundtvig can be seen at En Märkelig Vise om de Söfarne Mänd: An Old Danish Ballad.

There is plenty more to be found in the Forum and elsewhere.