Learn English – say “under number” to mean the unique code of a registered legislation

I don't think the word would be inherently interpreted with sexual connotations, but as is often the case, context is all important.

For example, your sentence is lacking context and begins with "Have you heard...?" which suggests some element of gossip. However, if you added context to that, such as:

Do you know who Jim and Tina are playing golf with?

Yeah, they've made a foursome with Jim and Tina.

The issue with your question is that, in isolation, the lack of context seems deliberate - as there's no indication for what purpose they've formed a foursome - and that's where the potential for innuendo appears.

Of course, people will also take cues from your tone and body language, so your meaning should be conveyed correctly, given that you provide sufficient context.

Just to make clear, I'm a British English speaker (and live in that region), but I think it's important to provide a global view. I'm not personally sure that the Americans would see matters any differently, but I do find issues of this nature fascinating.

In your example:

Notice that these examples fall under well-established categories of acceptable, standard English.

Think of a hierarchal chart with categories and sub-categories. In your example, "these examples" are sub-categories of "well-established categories", as far as I understand the context.

In such a chart, sub-categories are below categories, so fall under is correct.

In your second examples:

Voters fall into three main categories.
Students over 25 fall into a different category.

Here, the voters (or students) are part of (inside) the mentioned category. Therefore, fall into is correct.