These examples are all fine and would be understood by most native speakers.
I disagree with the linked site. Fever can be and is used for both mild and high temperatures.
"You have a little temperature" is OK because in this case temperaturetemperature is not countable, it's referring to the degree of fever. One can have a little temperature (fever) the same way one can have a little dirt on one's nose. You would not say you have "two fevers" unless you mean two separate occasions where you had a fever.
Another common expression is "running a fever."
Cathy was running a fever so we kept her home from school.
The text you quoted is not really correct about fever versus temperature and I disagree with the linked site. Fever can be and is used for both mild and high temperatures. It's easy to find examples.
When referring to a fever that is not high, you'll often hear the phrases "slight fever," "mild fever," or "low-grade fever." This is common usage, and not wrong at all.
Usually these mean a body temperature that's above normal, but below the threshold of of serious concern, usually up to 101F or 38C.
The common term for a high fever is usually just high fever and usually means a fever that's high enough to be of serious medical concern, generally above 102 to 103 F (39-40C.)
Medically, a fever is defined as a temperature above 100.4F/38C, but normal body temperature varies per person, and the ranges differ for children versus adults. These are guidelines, not hard rules.