Investing in stock will not hurt your f1 status unless you make profit out of it . So you can buy stock but selling is tricky . One thing is sure , you can not day trade while maintaining F1 status .

Pattern day trade is strictly supervised and regulated so if you are in process of obtaining gc , I suggest not to do day trade while investing is ok.

Have seen a junior IT guy suffering while day trading in h1 visa but haven't heard much about f1 .