'decent' - having manners/having common courtesy(sense), totally expected people to have manners. 'very kind' - doing nice things to people out of your way but not expected. These have slightly different meaning?

I sometimes say it but I don't hear it said by the younger generation in the UK. It may make you sound distinguished so feel free to try it out!

Yes, "That's very decent of you" is a pretty old-fashioned way of saying it. "That's very kind of you" is more common. You can also use "That's nice of you," which is probably the most popular, although this isn't as specific.

To me, "that's decent of you" doesn't sound very friendly. I would say that, for example, if someone did what society expects of them in a given situation. It could also be used ironically, so be careful. "That's nice of you" is a safer expression, which expresses that someone has done something, well yes, nice!

What about "basic rules of decency?" It looks like the concept would disappear together with the old-fashioned behavior to which it refers.