an interesting article, The Mysterious Downfall of the Neandertals, which concludes:

As for the last known Neandertals, the ones who lived in Gibraltar’s seaside caves some 28,000 years ago, Finlayson is certain that they did not spend their days competing with moderns, because moderns seem not to have settled there until thousands of years after the Neandertals were gone. The rest of their story, however, remains to be discovered.
So, the demise of this this particular group of Neanderthals cannot be placed at Cro-Magnon feet.

Two 2009 reports dealing with the Neanderthal genome suggest that the capacity for speech goes back to before the Neanderthal-Modern Human split in their "family tree" - here and here:

Analysis of the genome reveals that humans and Neandertals share genetic roots stretching back at least 830,000 years. Neandertals, the species Homo neanderthalensis, were humans’ closest relatives, appearing about 300,000 years ago and living in Europe and parts of Asia until going extinct about 30,000 years ago.

Anatomically modern humans, the species known as Homo sapiens, first appeared in Africa about 250,000 to 200,000 years ago.
and

Talk like a Neandertal

Neandertals may have had the genetic gift for gab, new research shows.

Analyses of the Neandertal genome reveals that the extinct human relatives had the same version of a gene linked to speech as humans do, says Svante Pääbo of the Max Planck Institute for Evolutionary Anthropology in Leipzig, Germany. Mutations that reduce activity of the gene, called FOXP2, also disable speech in humans.

Humans have a version of FOXP2 that differs by two amino acids from the chimpanzee version of the gene. Neandertals share the version of the gene found in humans, Pääbo reported at the human genetics meeting.

Many other genes may be required for speech but, in humans at least, no other genes have shown such a dramatic effect. The result could mean that Neandertals could speak, Pääbo says.

“From what little we know, there’s no reason they couldn’t talk,” he says.
I'll pass on opposite sex interactions - although it is mentioned in the articles.

Regards to all from the resident biochemist.