I will suggest this JavaScript implementation built by @Paul_Lamb here:
It is clean and simple, and should help you get started.
Re-reading BAMI would be a good thing. 
Never. Fully connected layers produce dense representations. HTM depends on sparse representations.
Yes, see our current discussions:
- Deep neural networks need boosting
- Application of HTM in today’s ML frameworks
- 2nd half (@subutai’s part) of recent Microsoft Research Talk
CHALLENGE! If anyone can do this I will reward you!