It sounds like a healthy plant. This is how they propagate. Also, they are feeding the mother so it can produce fruit. Once you pick the fruit, you can remove them and plant them separately and get more fruit.

Might be that particular variety. I've never seen sprouts like that coming from the fruit stalk. The 'pups' on the pineapples I've grown always arise from the base of the plant.

The ones that arise from the base of the fruit are called 'slips'. I think I read that slips are produced at the expense of fruit. So, you might remove them as soon as they arise. Some varieties of pineapples are more prone to grow slips than others.

I bought a named variety as plants at Lowes. They were Kona Sugarloaf. They did the same thing - tiny fruit and lots of slips. I never got even one fruit and finally got rid of them. Never had that problem with the plants from supermarket fruit. Maybe the Kona Sugarloaf is more adapted to Hawaii conditions.