быть осторожным/ой

Just a minor correction, regarding the rest I'm all ears too, it's always interesting to see someone else's viewpoint.

Also I would say that if you (a MAN) helped an old woman cross the street and then said "когда переходишь" it doesn't sound really polite, it all comes from context. An exception is if you said "когда переходишь улицу надо быть осторожнЫМ" intentionally resorting to the masculine-style ending, she might think that you are thinking about YOURSELF crossing the street and that you-the-masculine-yourself have to be cautious, and that's a good excuse for using a ТЫ-form while saying that to her. Anyway it's like walking a tightrope, the ВЫ option (without an explicit ВЫ) is also perfectly usable for generalization.