I'm struck by how generic the network in question is.
That's exactly the point of a convolutional neural network: it is intended as a general architecture for solving machine learning problems in computer vision, so you don't have to craft a customized architecture for each new computer vision problem you run across.
However, convolutional neural networks are focused on computer vision kinds of problems. The "convolutional" part makes sense in that domain, where we expect that there is some kind of "spatial symmetry" in images (a banana in the upper-left corner of an image looks the same as a banana in the lower-right corner, and the two should often be treated similarly). The same is probably not going to be useful in other domains, such as solving crossword puzzles.
Therefore, I would not recommend a convolutional neural network for your application. Instead of looking to computer vision and trying to crib off what they are doing, I suggest you spend some more time learning about the fundamentals of machine learning and deep learning; that will probably help you more.
For crossword puzzles, you will probably achieve much more success by building a customized algorithm that is designed specifically for that particular problem, rather than by trying to use some machine learning algorithm. Deep learning is not "fairy dust" that can magically solve every problem in computer science. They are good for very specific tasks (supervised classification, where you have a huge training set), but not everything; solving cryptic crosswords does not sound like one of the things I'd expect deep neural networks to be especially useful for.