I'm 29, single, and have absolutely no plans of having children in my life and I'm starting to think about this also.

In regards to finances, I think ultimately it involves finding someone who has some kind of fiduciary duty to you. How you find this person or entity will have to be determined by you. and this can probably change throughout the course of your life.

In regards to getting older, my plan so far has just been to keep as best health as possible (exercise, eating right, maintaining a healthy mindset) before getting to a point of decline. I'm still young, in pretty good shape and in good health, so this hasn't necessarily taken a precedent yet. If you're also in your thirties, you have a good number of years before you have to start making those decisions (end of life care), and who knows what life will look like then. I would say don't stress about it too much for now.

Probably not that helpful of an answer, but more so some random thoughts on the topic