Is it permissible to buy ropes from workers who take them from the port after unloading goods, and is there any doubt in that?

If the ropes are abandoned by their owners, then the one who takes them owns them, and their sale by him is valid. The general principle is that whatever is in the possession of a Muslim belongs to him if he claims ownership of it, and one should not inquire into the method of his acquisition, unless it is known that the property is stolen or usurped, in which case it is impermissible to take it. If the status of the property is unknown, the general principle is that it belongs to the one who possesses it, unless the person is known to have unlawful wealth, in which case dealing with him should be avoided out of piety. As for a Muslim whose affairs are concealed (i.e., not known to be involved in unlawful dealings), there is no doubt in dealing with him.