How to determine if the bootloader is locked
There's no fastboot for Samsung devices - Download mode is the semi-equivalent, except that it's only accessible via Odin/Heimdall. You will need appropriate drivers to get the PC to recognize a device in Download mode.

Most Samsung phones come with their BL unlocked or unlockable (notable exceptions are AT&amp;T/Verizon devices). To root these devices, turn on "OEM Unlocking" in Settings - Developer options (if the switch exists), find a custom recovery made for the device, and flash it with Odin/Heimdall, then finally flash SuperSU/Magisk. Alternatively, make a CF-Auto-Root package for your device and firmware version with firmware.mobi and flash it.