It depends how proficient you like to be, you could learn one song at a beginner level in just a few weeks or master in 10 years or more. It really depends what your goals are, a good piano teacher can really help with this process.
You're never too old to learn. Despite the saying you can't teach an old dog new tricks, there is increasing evidence about the brain's plasticity and ability to learn. So give it a go, it might even help ward off dementia.
You sure can! And if you want proof check out this video https://www.youtube.com/watch?v=UoLE31Y83LM to see Nicholas McCarthy's amazing skills with just one hand!