Explaining background info in a not boring or lecturing way?

"Show don't tell" is some of most frequently given advice in writing, but it also some of the most difficult to put into practice. I try very hard to communicate what is necessary without making it boring or making readers feel as if they are being lectured. One of the ways I do this is to have background information discussed in dialogue by characters, or having them ponder it in their minds. In each of these chapters, I have tried to be informative as well as entertaining. I want to know if you think I whether I accomplished that sufficiently in each of them, and what you liked and disliked about them.

clockworkmultiverse.deviantart.com/art/Part-2-Finding-a-lost-love-598478379
clockworkmultiverse.deviantart.com/art/Part-3-The-escape-599951142
clockworkmultiverse.deviantart.com/art/Part-9-Leaving-Home-Again-611608522
clockworkmultiverse.deviantart.com/art/Part-10-Trip-planning-612782551
clockworkmultiverse.deviantart.com/art/Part-13-A-Meeting-of-the-Council-of-Ten-631612949
clockworkmultiverse.deviantart.com/art/Part-14-Gussying-up-for-the-ball-634017284