What happens to my CPF after deceased?

If you've made no prior nomination or will, your CPF proceeds will go to the government.

I'm assuming here that you may be donating other assets to charity too, or have specific people you would like to have those assets; which means you'll need to make a will so that all assets will be distributed according to your wishes.

Great intentions to leave your CPF for charity.

YES, you can.

For those bigger charity group, you can approach them directly and they probably have a legal system to help you notify CPF board on the plans to leave your CPF for the charity group. Most charity organisation knows the paperwork for this.

For Medisave, you can use to a certain limit per situation. you always hear in social media of unfortunate cases where people have Medisave but is restricted by the maximum. Case by case, and you need social workers and proper appeal channels with doctor support.

PS: btw no intention of getting married doesn't mean you can't have a relationship with loved ones and having a great partnered life ;)