Is it okay that my contact lens is larger than my than cornea?

Yes, for soft lenses: Soft contact lenses are can be 1mm to 2mm wider then one's cornea. Gas permeable hard lenses are smaller. The eye doctor can fit one's lenses properly because he can see how the lenses sit on the cornea, and he sees how much the lenses move when the eyes move and when the patient blinks.

Of course: Thats how they stay on! hard lenses are smaller, though.

Yes: Most contact lens wearers use soft contact lenses, which are larger than the corneal diameter. This is noticed as a faint overlap on the white part of the eye, especially more noticeable when the contact lens is tinted. This larger lens adheres more. The other less frequently used contact lens, gas permeable contact, is smaller than the corneal diameter, and floats on the tear film of the eye.