For the first two sentences, “onto” my computer would be better. In the first sentence in particular there is the possibility of confusion — as written, you could be saying the photos are already on your computer and you’re thinking of transferring them to a flash drive, for instance. In both sentences “to my computer” instead of “onto my computer” works equally well. But not on, which implies the content is already there. For sentence 3, “on my computer” is correct. However, you have an extra “to”. Just say I’d better type up… “I’d better” is never followed by to. You did it exactly right in the first two examples. 😁