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.
You likely do not want to attempt this from Terminal but if you did you would want to use tmutil restore ... Read the manual page - for what that involves. The issue will be you will have to specify via the command line where in the time capsule snapshot the restoration will be sourced from.
For more likely success you probably should re-boot using the Recovery HD or some other graphical user interface mechanism intended for this kind of restore from disaster scenario that will guide you in finding the right snapshot as described in the Time Machine FAQ
Best Answer
Check if your password is longer than 15 characters, if it is just type the first 15.