I can't open the Photos app

Try to launch Photos while holding down the options key ⌥ . Hold down the key firmly while double clicking the Photos.app in your applications folder. release the key when you are seeing the dialog to select a library.

Does Photos show you a window with Photos Libraries to select from? Then click one of the libraries. At the bottom of the panel you should be be seeing the path to the library. Where is it?

Is the external drive currently connected? If not, plug it in and check again your Trash.

No it's not saying the app is in the bin, it's saying the library is in the bin. Search for that and restore it to its original location.

First, look in your Pictures folder for a file that is called, as léonie said, "Photos Library.photoslibrary." If it's there, double click on it to open that library in Photos. It may ask if you want to switch libraries, and that's OK.

Next, if that doesn't work, be sure Photos is closed and then option-click on the Photos icon. It will give a list of all the Libraries it knows about. You can pick one from there, or you can create a brand new one that's empty and ready for you to add pictures.

And next, if that doesn't get you the Library you're looking for, try searching for Libraries with the Finder search, like this:

Photos Libraries always end in ".photoslibrary" so that should show every one you have. Double click on the one you want.

In your bin look for an item called "Photos Library.photoslibrary".

You may have been using a library on an external volume, that is no longer plugged in. Do you have any external volumes connected?

An external hard drive or even a flash drive.