7000metre-high mountains

I wouldn't use any.

Why do you need hyphens at all?

I was taught to do so.
7000m-high mountainso (No hyphen between 'm' and 'high'.) Not sure about that one.

When numbers are used as adjectives, hyphens are required. Here's a page which explains it and gives examples:
Numbers as adjectives

Judging by that page, 7000-metre-high would appear to be the correct spelling, because high is an adjective joined to a number.

Thanks, Blickers.

Ate most native speakers particular about punctuation? I was told most native speakers do not even know what Past Participle is. In your experience, are the above true?

Yes. In fact, I would have to admit I would have to look it up to refresh my memory as to what a Past Participle is. Correct use of language has to do partly with education level, partly with the education level of your family and the people you know, and quite a bit with how much you read. If you read a lot of correctly written English, especially if you start when you're young, you just fall into the same patterns as you see written down and the correct form seems natural, even if you can't give details as to why.

I didn't know about the hyphen when numbers are used as adjectives, for instance. It is a somewhat minor point in terms of day-to-day usage, so I didn't know it. It was only when you said you were taught that hyphens were necessary when numbers were used as adjectives that I looked it up.

The second. To correctly form a compound adjective of measurement or quantity, join the number of the measurement "7,000", the unit "metre" (use singular) and the type of measurement "high" with hyphens:

Some 7,000-metre-high mountains
Some seven-thousand-metre-high mountains
A three-and-a-half-page report
A five-and-one-half-foot-long sign.

Thanks, Blickers, for the information.

Also: a one-hundred-thousand-dollar deficit.

Thank you.