Can I use "twrp-3.1.0-0_MOD_1-quark.img" with MM stock ROM and kernel?
Yes. This is official TWRP for all Quarks. You would just be replacing stock recovery with this custom recovery.
In fact, when you unlock the bootloader, the FIRST STEP after that is to install TWRP recovery to replace stock recovery. Only then, can you permanently root with SuperSu.
After that, then you can uninstall bloatware, or install custom ROMs or Xposed with Xposed modules.
But no one says you HAVE to do all that. You could just stop after installing TWRP.
TWRP custom recovery gives you the ability to make backups or to flash TWRP-flashable files.
Or are you talking about updating to this version of TWRP? You already have an older version? Either way, the answer is yes.