Quantified Self is in it's nature about dealing with epistemology. It's not certain that you will learn something about how an AGI works by doing Quantified Self but the potential is there.

A mathematical model of how human memory works that could be produced by looking at Mnemosyth data could also potentially matter for FAI.

FAI is a hard problem and therefore it's difficult to predict, where you will find solutions to it.

How easy it is to get funding for these kind of projects?

It very much depends on the project. I don't know how hard it is to get grants for the spaced repetition problems I mentioned. I however think that if someone seeks a topic for a bachelor or master thesis, they are good topics if you want an academic career.

The daily Anki score would allow other academics to do experiments of how factor X effects memory. If you provide the metric that they use in their papers they will cite yourself.

I thought that by "problems" you meant things like the millennium problems

I don't understand why anyone would want to work on the Riemann Hypothesis. It doesn't seem to be a problem that matters.

It one of those examples that suggests that people are really bad at prioritising. Mathemacians work at it because other mathematician think it's hard and solving it would impress them.

It has a bit of Terry Pratchett's Unseen University which was created to prevent powerful wizards from endangering the world by keeping them busy with academic problems. The only difference is that math might advance in a way that makes an AGI possible and is therefore not completely harmless.