I see five images uploaded. Looks good. The whole missing-picture-bug is merciless.
The leaf pattern on the trees I see looks like you got a true HC, which is similar to what I've seen several others who bought theirs at Lowes on the cheap. It's a surprise to see a 'big box' store actually get it right.
Here's what I would tell you about the growth:
Younger is worse when it comes to surviving winter. Trees are more hardy as they age (with many varieties). Smaller trees are easier to cover, though.
For the growth lag, I'd say this is typical of a young transplant. Some might say "give it fertilizer!" in order to perk it up, but that's going to inspire new green growth and green growth is even more susceptible to lower temperatures, so you're basically having it add more growth that will just die anyway (waste of energy).
In short, I would focus on letting it finish out the season, let it lie dormant till temps get down in the 38 F range overnight, then work on covering it up for the winter using any of a myriad of tips here at the forum. Let it bounce back next year with rapid growth after sleeping a winter in the ground.
For the dead branches... I'd just cut them off and trash them. Who knows why they died? Furthermore, for now, who cares? There are so few diseases that affect figs, and none of them I know of will kill entire branches (except exotic boring pests). Cut it off and move on. If you want to see if a borer attacked it, take the pruned branch and cut it down the middle to bisect it. Look at the inside for any missing pith (the white fluffy stuff between nodes) or evidence of something eating the insides of the branch.