Burn-in is not likely to be an issue on just about any modern monitor. Some IPS screens can potentially show a bit of temporary image retention under certain conditions, but are unlikely to experience permanent burn-in. Among common display technologies, OLED is the only kind of panel that can be prone to suffering from permanent burn-in, and you currently don't find that screen technology used in PC monitors, in part due to that reason. I would not be concerned about black borders any more than having the Windows taskbar on your screen for hours at a time every day. It shouldn't be a problem.
As for whether your screen is an "LED or LCD" display, it's both, as are just about all recent monitors. IPS, VA and TN are all types of LCD panels. LED refers to the backlight, and monitors switched over to LED backlighting from flourescent backlighting years ago. OLED, plasma and some other screen technologies are a bit different, in that each pixel is its own light source, rather than shining a backlight through an LCD panel, but again, you currently won't be finding those used in PC monitors (unless one is using a television as a PC display).