These two questions are only to be answered "in principle" (i.e. ignoring the difficulty of putting it into practice, which is a different question entirely).
Do you feel the need to respectfully use resources so that younger generations aren't more screwed over than they have to be?
Do you feel the need to "do your part" (however little that part may be in practice) for those people in the world who don't have basic human rights? (Clean water, nourishing food, the right to not be enslaved for any purpose, etc.)
I consider those responsibilities of every human, to be enacted in whatever way suits them personally, even if it's just the small act of voting for or against something, or being relatively conscious of where the things you buy are coming from... I don't think any one person needs to feel the burden of those who don't have basic human rights, but I think we owe the small effort here and there.
While I think the phrase "Now I'm reducing carbon footprints for 2" is a bit extreme, I do think it's a nice idea to be reminded that we are stewards of this planet. But living with respect to nature isn't about the children, it's about removing our personal arrogance and understand that we need our environment. We need to take care of our exploitations not for our children, but for ourselves. (If you think about it, if we don't, our retirement will be spent sleeping in sewage. Our children will have the opportunity to bail out and fly to mars)
On the subject of people who don't have basic human rights. There are good ways and bad ways of doing it.
The most fucked up way of helping another is through charity. While the third world charity funds sound wonderful and uplifting, this is extremely detrimental for the country. If they really wanted to better themselves, then they would. Honestly. They would seek out the help, they would fight. The troubles they have now aren't caused by their own doing, it's because we're over there giving them free money. We've enslaved them into a nation of beggars. Never give money because you think it's a good idea, because you give them the power the destroy themselves.
In all those decades of giving, there still isn't a transcontinental railroad in africa. why? how stupid is that? There's no infrastructure in all those years of money giving. This is because they aren't interested. Not seriously enough to do something about it.
Africa: the next chapter
The good way of doing it is to leave them alone, or get your ass in there and help instead of talking about it and having that cover your guilt. It doesn't help. Follow in the footsteps of Neil Turok and how he wants to help the first african einstein.
Neil Turok makes his Ted Prize wish
All in all, the country must be able to lift itself out without any charity. It must do it through trade. Otherwise, you'll have a spoiled child looking for the easy way out.
Basic rights are earned and fought for, never given. If given, it comes in the guise of freedom and compassion, but with the intent to enslave them all. You owe them the freedom to help themselves struggle and grow in their own way as we have fought and struggled. Then party with them for their well earn pride.