If I attach information e.g. date, place, people to a photo through Photoshop Elements and then send that photo to someone else, can they access the information? Or do they need to have Photoshop elements too?
It depends. You can write the tags to the file's metadata (using Ctrl+W), but there is no consistent standard for reading the information. Keyword tags can generally be reviewed in Windows file properties. But if you are using the Organizer's People, Places, Events tags, these may not be fully visible and any face recognition showing faces will not be transferred even to another computer using Elements.
Keyword tags can generally be reviewed in Windows file properties.
...they can even be displayed in Windows Explorer by selecting the keyword column in details view, so you can sort the files by them or see a bunch of them at once. Just as a quick add-on to Greg's hint.