- How do I get it out?
Completely remove screws outlined in yellow
Insert thin sharp object like kitchen knife, x-acto, box cutter... on blue arrow to cut the paint sticking the fixture to the ceiling.
Pull on it.

If it pulls out, congratulations. If it does not, you're in trouble, because there are no other visible screws for the purpose of fastening it to the ceiling, so that could mean whoever installed it glued it to the ceiling, probably with silicone caulk or MS. In this case, you're gonna have to spend a while artfully slipping the blade of your box cutter around the perimeter to cut through the glue without making a disaster on the painted ceiling.
I'd recommend starting with a fixture that is somewhere like a corridor, where screwups will be less noticeable.
You can also remove the 3 screws in red, maybe you'll find the secret screw to take it off the ceiling, who knows.
- What kind of light is it?
It's garbage.
- What could be the problem?
LEDs work fine when hot, but not for long. To last, they need to be cooled. So you see the brand new light working well, and it is cheap, but the effects of cheap cooling (or no cooling) only show up after a few months when it mysteriously stops working. Cheap bulbs are easily replaced, but this type of light needs a bit of labor to install, plus the hole in the ceiling, so it's not worth it to go for cheap.
First there needs to be thermal paste for good heat transfer between the circuit board and the sheet metal. After you remove the three red screws, I'll bet you will find just a tiny drop of thermal paste under the LEDs that survived, and none behind the ones that fried.
Then, on this type of fixture, the heat from the LEDs has to travel horizontally through the steel sheet metal to the edge, and that doesn't work. First, steel doesn't conduct heat very well, that's why heat sinks are usually made of aluminium. Second, heat travels efficiently through the thickness of sheet metal, because sheet metal is thin so it doesn't have very long to travel. But in the other direction, there is much more distance, and little cross section. So the round outside part of the light, which should be the heat sink, isn't.
Some lights have a heat sink at the back to dump heat in the space above the ceiling, like the one below. That only works if it's not full of fiberglass.

Before deciding on a replacement, you have to check what kind of hole you'll find under it. Then decide whether you want a round mini panel like in the screenshot above, or perhaps some GU10 downlight, or something else. If you have a lot of holes, it's worth it to find something that fits, or at least lights that cover the holes.
These days I'm installing Osram 4058075608290 3000K 90CRI GU10 spots. They're cheap and they last, if the fixture allows airflow for cooling.