Checkrom is xwla4 so use the xwla4 cfroot kernel. As for rooting without a computer I don't think so.

 

It's never a good idea to flash a kernel just after flashing a new rom. Some kernels come with auto rooting, some so not. Boot up with the bundled kernel next time, then flash the kernel of your choice.

There is no software that could be run on your phone to root, as it would require root access to be able to do so in the first place! It's odin or nothing to do this I'm afraid. Once rooted you can use mobile Odin to flash other kernels, modems roms etc if you require.

 

Whatever state your phone was in at the time you performed the backup is what you will get when you restore. It's basically a complete snapshot of your phone.....almost:
Only the modem will not get saved, so if you change modems between backup and restore you will still have the last one you installed