S4 here too! The last great flagship, as far as I'm concerned. Removable battery (just ordered another!), headphone jack, microSD slot, USB OHG, HDMI/MHL out, glove-compatible touchscreen, and small enough to fit the hand.
I'm gonna keep these things running as long as I can, because the prospect of replacing them with something a decade newer but inferior in every meaningful way is simply sad.
LineageOS is the only reason I don't loathe the whole Android ecosystem, to be honest.
TBQH I've never been quite clear on what it means to root a device. I just run Heimdall and load the files they specify, plug the device in, and a few minutes later, it reboots into Lineage.
To install LineageOS, it is enough to unlock the bootloader, which permits the installation of operating system images that have not been signed by the manufacturer (e.g. Samsung).
Rooting permits applications to have more control over the device at runtime. Some devices require the bootloader to be unlocked to enable rooting, and others do not.