Can the deceased supplicate for someone who did him a good deed without his knowledge during his lifetime, and does the doer of good benefit from this supplication?

You are permitted to perform Umrah on behalf of your grandmother who is unable to travel, provided that you have first performed Umrah for yourself, and that it is with her permission. However, if you intend to perform Umrah for yourself and then donate its reward to your grandmother, her permission or notification is not required. As for a deceased person supplicating for a living one, the general principle is that the deeds of a deceased person cease upon their death, except for what has been explicitly stated not to cease.