What is the ruling on opening a shop for games such as table tennis, billiards, and foosball for specific amounts of money depending on the time, and is it permissible to play these games in the first place?

There is no objection to opening a toy store, provided it is free from forbidden things such as music and gambling. Those in charge of these stores should utilize them for inviting to Allah by closing them at prayer times, playing beneficial materials, and distributing useful pamphlets. By doing so, they will have attained the good of this world and the Hereafter.