There, There!

Dear Experts,

Is it correct to say -

1.There is a cat on the roof sitting.

2.There are many free English web sites available on the Internet.

kind regards.

Curiosity always pays.

There is a cat sitting on the roof.

It’s not the roof doing the sitting.

You might see this kind of construction, though:
There is a cat on the roof, sitting and staring. (The cat that is on the roof is sitting and starting)
There is a cat on the roof, just sitting there. (The cvat that is on the roof is not doing anything other than sitting)

Your second sentence is okay.

Thank you very much Bees, your are a genuine expert of English.

These little sentences with your expert guide improve my command of English a lot.

kind regards.

Curiosity always pays.