What is the ruling on the rapid buying and selling of shares on the same day or hour, given the ignorance of what goes on behind the scenes and how quickly shares are registered in one's name, and is it permissible to trade them over long periods, such as months, taking into account the impact of this on prices?

It is permissible to invest in the stock market (bourse) under certain conditions, including that the company's business must be permissible and it must not deposit its funds in riba-based (usurious) banks. If you purchase permissible shares and they are registered in your portfolio, it is permissible to sell them immediately thereafter. It is not permissible to manipulate stock prices by offering large quantities for sale to lower the price and then buying them cheaply. However, if the investor does not intend to manipulate, there is no harm in selling or buying any number of shares at any price and at any time, as long as their investment is in shares of permissible companies.