LSTMs - Carousel of Error
One tool that may be helpful is Aiden Gomez's blog post. Its strength lies primarily in the fact that he runs through a toy/numerical example, which when paired with the original paper/thesis , serves as a great foundational tool.

I did take a look at the site you mentioned in your other question, it's actually an excellent resource. I'll hop on over and try and clarify what I can for you when I get a chance. It looks like you've misunderstood/overlooked notation which can happen since there are so many components involved. 

It may also be worth taking a look at some code. Siraj Raval has a great video on LSTMs and includes the code in the link I've included. No libraries. I wouldn't dive too deep, but it's a great way to see the inner workings of the network.

As far as the CEC goes, there is a reddit post. If you're looking for a more rigorous handling of this topic you can either reference the original paper or often cited paper: On the Difficulty of Training Recurrent Neural Networks.