I’m not sure, but from Pauly01’s most recent post, I suspect he has a fuse box (like your first photo) in which the fuses have been replaced by screw-in circuit breakers (like this). To reset the breakers, you press in the little button.
ETA: Simulpost with Toledo Jim!
Okay so in that extended cord outlet, i have laptop charger always connected to it, same with the lamp though lamp is only open at night and one other outlet is avaiable and that was where i put the heater on it.
So if i open the heater, does that mean i have to make sure to never use this extended cord outlet ever again and always use the 2 that are near my bed? Those were the 2 outlets that still worked when i had this issue.
Also im pretty sure the laptop charger never caused this problem as its always plugged in. I had the heater plugged in most of the day, it was just when i went to cook rice with the rice cooker and when it was almost done cooking when all of these things went out. However, i did the same thing the last 2 days but this didn’t happen. By that i mean i had the heater on connected to that extended cord outlet along with laptop charger connected and of course cooking rice with the rice cooker.
I guess just never use that outlet ever again for the heater? What about use it for the heater but if i then use the rice cooker, i then just make sure i unplug the heater or plug it into the outlet near my bed?
This got me very stressed out. Reason is b/c i actually found out i could connect my laptop charger to a wall outlet but i would have to take out of the plug that goes on to the TV which means if i dont want to move my monitor/laptop to a eating table, i would have to unplug the tv plug so i cant have tv on and have laptop charging while in the computer desk.
Thanks for the info - I’d never seen one of those before. I’ve lived in places with old fashioned straight-up fuses and new breakers, but not the retro-fit. Very interesting!
I think you just shouldn’t have the heater and rice cooker on the same circuit at the same time. Probably the easiest thing would be to unplug the heater when you use the cooker. Your apartment shouldn’t cool down too much during the half hour it takes to make rice.
As Capt Kirk mentioned in post #7, the rice cooker and the heater are the two big current draws, the best way to prevent this in the future is just not have both of those on the same circuit. Things like the charger and the TV (unless you have 75" rear projection TV) don’t really use that much current. My 42" LCD TV uses less than 2 amps. A 1500 watt heater is nearly 11 amps all by itself, and the rice cooker could well be another 8-9, so a 20 A breaker would be close to the edge.
ETA and another simulpost!
I picture is worth a thousand fuses. Think of how much quicker and easier we could have answered the question if we had a pic of the box in the first place.
Pauly01, get a camera! 
one of the safety issue with those “fuse replacement circuit breakers” is that the button has to be able to fully pop out to allow the breaker to shut the circuit off (as intended to do for safety). some old fuse boxes had the door too close to the fuses to allow this. to allow the breaker to safely trip you couldn’t fully close the door.
You should be able to find wattage ratings on your rice cooker and heater (and anything else that draws significant power); look at inconspicuous places on the bottom or back. Add them up and try not to put a total of more than 1500 watts on the same circuit (using that as a limit gives you a margin for error; you’re not likely to pop anything if you go a little bit over, but the more over you do go the more likely you’ll pop a breaker).
BE CAREFUL about using an extension cord with multiple high power sources; I hope you are using a heavy-duty one!
Pauly, each breaker is connected to a wire with one, or several, outlets and appliances connected to it. You could overload a circuit by plugging heavy loads into two different outlets if they are connected to the same circuit. Try to plug them into outlets that are away from each other, or in different rooms.