Is working in a grocery store considered permissible (halal), and what about a house bought with money from selling songs? What should be done about the house? And why do the relevant authorities not prevent the opening of shops that sell songs?

There is no blame upon you concerning the shop purchased with money earned from selling forbidden songs. However, you must dispose of the unlawful money if you were aware of the prohibition of selling songs when you acquired it. But if you were ignorant of its prohibition when you earned the money, then some scholars permit you to benefit from it. As for selling forbidden songs, it is impermissible because they contain music, or are performed by female singers, or incite immorality. You must estimate the proportion of the unlawful part from the price of the tape and dispose of it for public welfare or for the poor and needy. The reference for the issue of preventing the opening of shops that sell forbidden things is the responsible authorities.