100,106 (At one point, it should be noted, I came to 100,010 instead, but the first number should be correct.)
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I think 105.
Nine of them
It is any one of infinitely many numbers of the form 1407.92nnn where nnn... is any string of digits other than all 0s or all 9s.
79
They can. And if you include repeating 0s and repeating 9s, then all rational numbers can be written with infinitely long repeating digits.