Time Machine works at a file level, with no facility to perform incremental changes within files. As such, your Sparsebundle may be backed up in it's entirety every time it changes in the slightest, depending on how large it is. Of course, you have to wait up to 1 hour (+the time it take to make the backup, depending on how large the queue is and where your file sits in it) to ensure those changes are included in the backup. Also if your Sparsebundle is in use (mounted...) then it may well skip it until the file lock is freed
This is a terrible system, and one that we might not see change until the underlying filesystem is suitable upgraded (or replaced) to include such useful facilities as incremental block level changes rather than simple file level ones, and/or deduplication etc. One early victim of this scenario were users who used the original Filevault system for encrypting their home folders. Time Machine would not backup their home folders until such time as they logged out because the Sparseimage file was constantly locked by the fact the user had it mounted. And even when the user did log out, it would proceed to make a hugely inefficient backup of the whole thing again and again - on the assumption that they simply logged out and didn't just turn off etc... Not very clever. To try to ameliorate this the Sparseimage spec was ammended to allow for Sparsebundles. Instead of a single big file, a sparse bundle is a bundle (directory) containing a number of files called bands, each in the order of 8 MB in size. This means even though to the end user the sparse bundle appears as a single file, it is composed of smaller files. As of Mac OS X 10.8, the bands are 8.4 MB each. When the content of the image changes, one or more band files is changed, created, or deleted. This allows backup software (such as Time Machine) to operate more efficiently, but it's just a bodge to attempt to mimic block level changes in individual files, which is limited to 8Mb "blocks"...
So to answer your questions directly, 1) it handles them properly, where properly means the same as any other file, it's just that your particular use (leaving it open and mounted) may not result in efficient backups that are taken regularly, especially if you rarely unmount the file, and 2) yes, you will need to pull back the whole file to view it's contents. The TM restore interface is also file specific. It may have quick-look plugins to allow you to view simple files inline like JPGs etc, but not for a complex file like a sparsebundle.
On the bright side, you already have a licensed copy of ChronoSync, which is super useful, and I would continue to use this to perform incremental backups of your sparsebundle whilst it is mounted, you can use the same drive as your TM images too.
No - Power Nap is extremely selective about what activities it will take on and thus far, no third party hooks or API is provided by Apple to allow someone to easily modify what happens when the OS wakes from a nap.
Clearly, someone could reverse engineer things and come along with a solution, but that hasn't happened yet. If they do, we can surely come with a better answer but at the moment you get the behavior out of the box which isn't going to accomplish what you ask.
Best Answer
This is going to be a throughly unsatisfying answer, but it comes down to the fact that random network drives were not meant to be used as time machine backup targets.
I'd wager one of the things you did in your guide was to run a terminal command along the lines of:
Unsupported being the watchword here.
I've run into this exact problem myself, but only when backing up to network shares.
Usually what it takes to break Time Machine out of its funk is to completely disable it (toggling the switch to off in the preferences pane), unmount your network share, remount it, and then re-enable time machine. The system is smart enough to see that you already have backups in the bundle file and you won't lose any data.
Still - you're playing with your safety net. If the contents of your machine are super important, please pick up a time capsule so you don't wind up with a nasty surprise some day.
I've no idea what triggers this behavior - it appears to be completely random.