You can use Kaggle’s Search bar to narrow things down.
Just search for a good keyword, like “medical”, and then you will see
Searching for medical within
followed by some options to select. You can choose “Competitions” and that should narrow down the possible datasets for you to go through. You can try different keywords as well to find some of them.
Whether or not a dataset satisfies all your requirements is really dependent on what’s available on the website. You will have to rely on different resources if Kaggle doesn’t help beyond a point. Like -