As New-To-IT said, if you want to be 100% sure all traces of the photo are removed, you should wipe the cache.
However, to answer your first question, whether changing the wallpaper automatically deletes the previous wallpaper from the location where the system stores the current wallpaper:
Yes. Or, more accurately, the previous wallpaper is overwritten with the new one, because the same filename is always used. The current wallpaper is stored in an image file that's actually named "wallpaper". When you select a new wallpaper, the image file you select is copied to the standard location (either /data/system/users/<userid> or /data/data/com.android.settings/files, depending on which version) and given the same filename, so the previous "wallpaper" file is overwritten. (Of course, that doesn't delete the image from the original location, but you've already deleted it from there.)
Regarding your second question, it's not entirely clear what you mean by "possibility of being hacked". If you want to know whether anyone else who has physical access to the phone can access the file, the answer is that as long as the phone is not rooted, there's no way to browse to the current wallpaper file. But yes, there is a possibility of accessing the file by hacking, of course: it's possible to root the phone and then access the file. But the answer to the first question makes this question moot, because as long as the image is present in that system location, anyone who has the phone can plainly see it as the home screen background, and if you change the wallpaper then the image is no longer stored there.