This counter tells you how long a piece of writing is: words, characters with and without spaces, sentences, paragraphs, and how long it takes to read or read aloud. That is what most limits are actually written against — a 2,200-character cover letter, a 160-character meta description, a 280-character post, a five-minute talk. It also lists the words you use most, which is a quick way to catch a phrase you have leaned on three times in two paragraphs. The text is counted as you type, in your browser, and is never sent anywhere.
No. Counting happens in your browser as you type. Nothing is sent over the network and nothing is kept once you close the page, so drafts and confidential documents are safe to paste.
A word is a run of characters separated by whitespace, so hyphenated compounds count as one and numbers count as words. This matches how word processors count, which is what most submission limits are based on.
The "characters including spaces" figure is the one those limits use. Note that platforms sometimes count an emoji or an accented letter as more than one character, so leave a little room when you are near a hard limit.
It is an estimate from the word count at 200 words per minute, which is a common average for adults reading prose on screen. Dense technical writing reads more slowly and light copy more quickly, so treat it as a guide rather than a measurement.
Character counts are accurate for any language. Word counts are not meaningful for scripts that do not separate words with spaces — for those, use the character count, which is what limits in those languages are normally written against anyway.