If the film is completely overexposed or if it can be developed successfully boils down to one thing:

Did you rewind the film in a dark-room or in a dark room? If the room was a lightproof room (a dark-room) with ABSOLUTELY no light in it, the film will be good.

As you said, you could not see any change on the film, I assume that the room was just somewhat dark (By the way, you cannot see the changes of the film until it is developed). In this case the film material is completely overexposed.

If you had opened the camera, immediately closed it again and the used the rewind of the camera, the first images might have been shielded by the film material around it - in your case, the roll is pretty surely gone.

To the second question: You can and should roll back the film completely into the cartridge. The developers are going to open up the cartridge anyways or use a extractor tool, assuming we are talking about common 35mm film cartridges.

The 35mm cartdriges open reasonably easy, when you just smash them on the table, with the protuding knob down. The lid of the other side then just pops off. Note that this is usually done in a lightproof room or in a lightproof bag.

But maybe there are still images?

If you want to make super sure, you can let them develop the negatives ONLY - without ordering prints. You will probably receive an almost black strip back (as in the negative, overexposed areas become very dark). This way you can save yourself the money to order 36 almost completely white sheets of photo paper, while still checking for anything left to recover.