Yes. Deleted text messages are not physically removed from your Android device. This fact enables them to be recovered by connecting the device to a computer and using data recovery software. The software will treat the Android as a disk on which it can restore deleted files including text messages.
This answer depends on the carrier that you use. The text message detail is kept anywhere from 60 days to seven years based on your cellular provider. The actual contents of the messages are only kept by a few carriers, with the rest of them not retaining this information at all.
Yes. Images that are sent as attachments to text messages can also be recovered using data recovery software. Since an image takes up more storage space, there is a greater possibility that the space it had occupied has been overwritten, making it impossible to restore the photo.