First let me say that FOG is not a backup tool. It never has been and it never should be. Yes you can do that for backup and restores, but understand its a disk level backup and restore. You can’t easily restore a single file from a FOG archive. With that said, there are indeed people that do use it to backup systems.
But I think you would be better served by another tool. For endpoint backup where we need to ensure we have a solid backup, we use Veeam Endpoint (free). This integrates well with our Veeam B&R for our virtual environment. BUT I also use it on my home computers (both windows and linux) to backup to my NAS. Understand this is all for free. There are some limitations like only backups once per day, and no notifications for backup failures and such. That stuff is reserved for the paid for model. Users can initiate a back or restore from the desktop tool.
As for inventory and package deployment, I would look at PDQ Deploy and PDQ Inventory together. They have free models, but their paid for versions are reasonably priced and well worth it.
Both of those solutions above will keep you in the windows camp, if that make you happy to live there.
Can you make fog do what you want, yes but you may need to do some programming and tweaking to get a clean solution.
As for your question about pxe booting on next reboot. If you are using Dell’s yes you can do that. With the dells you can use the command and control utility to update the bios to pxe boot on next restart. This switch can be set from a power shell script or vbscript deployed as a fog snapin or pdq deploy package. There are a number of way to make this work. It just depends on the amount of effort you are willing to put into a “for free” solution.