Well, again, you don't need to sign into iCloud.com for your issue. I think there is some confusion about how iCloud is used for your photos.
Since you don't have a laptop, you are not using iCloud Photo Library, there is nothing on iCloud that you can access anyway.
Open the Photos app on your iPad and click on Albums. Scroll down the list of albums and you should see an album titled "Recently Deleted". Click on that album and you should see the photos/videos you deleted. Click on the Photo/Video and at the bottom of the screen you will see "Recover". Click on that to recover the deleted item.
The only thing that iCloud has in the way of Photos is your Photo Stream and, if you do iCloud backups, it also has a backup of your Camera Roll photos that were on your device when the backup was done. You cannot access either of these items directly via iCloud. Your Photo Stream is on your device and your Camera Roll can only be recovered by restoring your device to that backup. But you do not want to do either of these things in this situation.
Again, find your Recently Deleted album and you will be able to recover any photos/videos that you have deleted in the last 30 days.
And one clarification:
Photo Stream is a streaming mechanism that is housed in iCloud (but not directly accessible through iCloud.com) that is used to share your last 30 days or 1000 photos taken with any of your devices signed onto the same iCloud account with eachother. So, if you had both an iPad and an iPhone and you were taking photos with both of them, your Photo Stream would have the photos you took from both devices in one place. You would be able to see your iPad photos and your iPhone photos on both the iPad and the iPhone in the Photo Stream.
You may see more than this limit of photos in your Photo Stream because they will accumulate on your device until you sign out of iCloud on your device. Once you sign out of iCloud, you will only get the last 30 days or 1000 photos because that is all that iCloud keeps, so that is all it will be able to re-download to that device once it is signed on and reconnects to iCloud.
Camera Roll is just like a real camera roll in a camera. Any photos you have taken on the iPad will be in your Camera Roll and will stay there until you delete them. You can only see the photos taken on that device in the Camera Roll. So, if you took photos with both your iPad and your iPhone, you would only be able to see the iPad's photos in the iPad's Camera Roll, and you would only be able to see the iPhone's photos in the iPhone's Camera Roll.
Cheers,
GB