OK, here's my take on the wearing of the cross: there's been quite a resurgence of Christianity within Russia over the past few years. Wearing the cross could (Putin hopes!) win him acceptance (& votes!) from Christians.
As for the constantly bared chest: It appears that this sort of display goes over a treat with young Russians. Putin, man of action! Older, but sort of strong & "youthful" looking. (Apart from that, he may be suffering some sort of mid-life crisis & needs to reassure himself of his own attractiveness, virility, etc, etc, etc ...
)
I think it's all part of a calculated PR exercise.