When we erroneously treat the well, (Type I error), or reject a true null, do we wrongly act on a false?

When we erroneously treat the well, (Type I α error), or reject a true null, do we wrongly act on a false? yes or no and please explain this to me

When we fail to believe the sick (Type II or β error or fail to reject a false null, do we wrongly act on a false? please explain