Note that you ask not one, not two, but three very different questions in this meta-question.
Can I post more than one claim?
We discourage it.
Consider what happens if someone can answer one of the claims and not the other?
In this very meta-question, if this was the only question you had asked, I could have closed it as a duplicate of Multiple claims in one questions, and I would have added a comment also pointing out this question which tackles the "closely related" issue: When is the number of statements to verify too large?
Because you didn't, this question is only answerable by people willing to take on all your questions
Are notability links necessary?
Again, if this had been a separate question, it would have been closed as a duplicate of a FAQ question: FAQ: Must all questions be notable?
This is also discussed in the FAQ: Welcome to New Users.
Note the date of the first of those links: June 2011.
The example question you chose as your template (Are there more English speaking people in China than in the USA?) was posted shortly after, before we started enforcing this rule. If it was asked again today in the same format, it would be closed until notability references were added. You should not use this as a precedent of a good question.
Would it be on-topic if I posted an article/study making the claim?
Yes, but I am calling your bluff here, because I do not think you will find any study making the claim as you have currently described it. If you find a relevant article, and adjust the question to match what they are claiming, then, yes, it will probably be fine.
If you find a high-quality study making the claim, hopefully you won't even need to ask because it will be the answer you are looking for.
Asking better questions
A good exercise for fixing a question is to imagine what a great answer might look like, whether the answer is yes, no or something else. How would a scientist who was researching the subject come up with an answer?
Let's do that for the two questions mentioned:
Why the English/Chinese question is bad
I can imagine a scientist sampling people in the USA and China and testing their language skills, but what does it mean to speak a language? Being able to count to 10? Being able to understand a story in the newspaper? Being able to translate technical documents between languages? Are these questions culturally-biased? This is an unclear question.
Normally, the solution is to look at the context of the claim - follow the notability link and try to understand what the original claimant meant. But with no notability link, there is no chance to do this.
The answerers have to guess at what was meant, which makes the answers less than definitive.
Why the breast attraction question is worse
What would you measure? If you took a random man and a random woman, and wanted to know which one found the opposite's breasts more attractive, what sort of test could you use?
Do you get them to rate it on a scale of 1-10? How would you factor into account that society has conditioned them to value bodies differently and to express certain views to be consistent with femininity and masculinity? Should that even be factored in? How do you factor in accessibility? Should that even be factored in?
The question makes little sense, AND we have no notability reference to determine what was meant.
There is also the issue that there is no evidence that the claim is widely believed. Answering a question on Skeptics.SE takes time and effort, and we don't want to squander that on questions that are irrelevant because very few people believe there is true. If you chat in a bar on an average night, you'll hear plenty of hare-brained claims, but we aren't interested in chasing down each one and researching it for no return. We want to have an impact. A notability reference can help us establish that.