Is it possible for an elderly person to become an accomplished pianist?

Yes, as long as you have a certain book or books that you are teaching form and can play the majority of those songs proficiently well, you should be fine. And if you are averaging eight to twelve hours, then you should be in good shape. If you want to learn how to play fairly well, look around for a teacher that specializes in older students. There is bound to be some around and you should be able to teach fairly advanced young students in a year, at most.

I think that it is great that you want to learn piano and teach it to others. My first piano teacher was older and she wasn't very advanced, some of the songs I played, she could play some of but not up to tempo and not super great note accuracy. But, why I liked her is because she was very passionate about teaching me. She would go on youtube and listen to my songs several times until she understood exactly how they went. The only thing she ad totally mastered was hand position and we got along great and that was all I needed to get a start in piano. Thus, the moral of story was that you should worry about being able to keep up with your students but don't entirely focus on that. Try to be fun, interesting, and dedicated and I promise your students will love you and the piano more then if you focused entirely on how the music should sound according to Bach or Beethoven.

You could become an accomplished pianist without lessons but it is most likely easier with a teacher to guide you. Also a teacher is good to know proper playing techniques. I'm not sure if the piano has any hard techniques, but you don't want to form bad habits. I've played the flute for eight years and i have a really bad habit of my fingers going over the edge of the keys. My old flute teacher never told me to stop so now i have a bad habit. My current teacher always reminds me but habits are hard to break. So i suggest some lessons to see if you have the correct techniques or hand positions.

I can't fault you for trying .How fast you can develop remains to be seen. Go for it!

As to teaching why not wait until that golden moment when you think you are ready and start with a beginner to see.

Being a great teacher does not mean you are a concert pianist.Great teachers are those who get across to their students.

I am an 81 yr old who played professionally at age 13 , got two university degrees , taught in public school in NY for 30 years and am still playing in a wind ensemble in Texas.

Definitely

The main thing is to know what materials you will use, what to do when something doesn't work with a student and to stay ahead of what the student has learned.