1) I've never heard anything about it being rude to sign your name... I mean, we're talking about foreigners right? Just about all Japanese take it for granted that foreigners don't have a "hanko" (name stamp) and so straight away ask us to sign. I've had some very suprised looks from bank staff etc when I produced my custom "Justin" hanko. As for my wife, she never signs her name unless it's for registered mail (as Andrew said) or for credit card transactions. So as for it being rude to sign your name... I don't think so.
2) Mmmm, a bit of a grey area here with the unemployment statistics. I guess amongst older people the unemployment situation was a bit taboo, and talk about why Mr Watanabe comitted suicide centers around "personal crisis" and never solely blamed on unemployment. On the JR Kobe train line just last week there were two (2!) suicides where people jumped infront of trains... yes, this is common in Japan. Unemployment related? I don't know, but bear in mind, the pressures of living in a society were status is EVERYTHING, life can get a bit shitty if you're at the bottom. But with the younger generation, unemployment - amongst my students at least - has almost become "cool", like they are rebelling against societies expectations or something.
I haven't answered your question well SKY, so I'll shut up now...