In the Slang Dictionary, I found the expressions.

[toilet terms]

1. Mom, I need to go number one.
2. Mom, I need to go number two.
[In the slang dictionary]

3. Mom, I need to go number three.
[I coundn't find this one in the slang dictionary, but it was in the urban dictionary.]

Do people or children use these expressions when they need to go to the bathroom? Is #3 used? Is #3 the same as #1?

Yes, these expressions are used. Number one means to urinate. Number two means to defecate. I've never heard of number three.

Stupid kid at the toilet with mom's phone while pooping

Yes, people, including children, may use expressions like "number one" and "number two" as slang terms when they need to go to the bathroom. These terms are generally used as a polite or euphemistic way to indicate the need to pee (number one) or to poop (number two).

However, the term "number three" is not as commonly used and may not be widely known. According to your information, it was found in the Urban Dictionary, which is a community-driven online dictionary that contains both slang and informal language. The exact meaning of "number three" may vary depending on the source or the individual using it. Without further context, it is challenging to provide a definite answer to what it means.

It's worth noting that slang terms can vary significantly among different regions, age groups, or social circles. It's always best to consider the context and the people involved when using or interpreting such expressions.