Number of firms in Long Run

In a competitive market, is it possible to know the change (increase/decrease) in number of firms in the Long run with a positive shift in demand for increasing costs case?

Yes, it is possible. In the long run, firms enter until they break even. Suppose firms are symmetric. Then for each firm the break even condition is that the average costs equal the price. This is because the price is equal to the average revenue. The average revenue is given by $px/x=p$ where $p$ is price and $x$ is quantity. If revenue equals costs on average, then there are no profits left to be made and this is the equilibrium number of firms.