Definitely not true. Historically, it's been one of the ways they attract (and scout) top talent.

I don't think that's true. Many big companies contribute to FOSS in ways that aren't just to attempt to lock people in. Often it's because they use the software and don't want to maintain patches forever - everyone wins if things actually get fixed. Or even because they just want to be known as a good place to work.

No. Microsoft and facebook are the try-hardest by far.