2016 Kia Rio Stalling/Overheating

Generally any engine issues severe enough to cause stall and/or acceleration issues will usually set a trouble code in the On-Board Diagnostics (OBD-II) system. Is your "check engine" light on? If so, there will definitely be one or more trouble codes registered, but even if it isn't, there still should be a code that can be read.

Most auto parts stores here in the US will hook your car up to their diagnostic scanner for free and give you any codes found. That would be the first step I would try to diagnose the issue. There are also bluetooth dongles you can purchase that can be used with free apps on your phone that can give you that same information; those dongles can be very inexpensive; I've seen them under $5 USD on places like AliExpress.

Anyway, however you can get them, once you have the codes come back and add that information to your question and we'll see what direction that takes us.

With regard to the overheating, there are a lot of possibilities here. Have you checked your coolant level? Open up the hood and see if the fans are running; a failed fan motor could allow it to overheat at idle. Keep in mind the fans run on demand, so they could be turned off if not needed at the moment. If you have A/C, turn that on; it will automatically turn on the fan(s). Check those things then come back and let us know what you found.

The P0300 is a general misfire code, while codes P0302 and P0304 indicate misfires on cylinders 2 and 4 respectively. I see you have code P0130 down twice; by chance did you mean the first one to be P0301 instead? That would be a misfire on cylinder 1 as well.

P0130 is the upstream oxygen sensor, the one before the catalytic converter; your engine computer doesn't believe some of the readings it's getting from it.

P0420 is also related to the catalytic converter; it says it's not working efficiently enough - it gets that information by comparing the upstream and downstream oxygen sensors.

Finally, P0455 says you have a large scale leak in your EVAP system; that's the system that scavenges fuel vapor and returns it to the gas tank.

The one thing I can see that all of these have in common is that they can all be caused by a vacuum leak. You'll want to check all the vacuum hoses, along with the air intake hose between the MAF and the intake manifold, looking for leaks. You can also try a can of starting fluid or brake cleaner; spray the hoses as the car is running. If the engine speed picks up you've found a leak. Otherwise listen for any hissing noises or try spraying hoses with a solution of dish soap and water, looking for bubbles.

Engine coolant inside the passenger compartment is almost always caused by a leaking heater core, the hoses leading to it, or possibly the control valve that regulates the flow of coolant inside the heater core. Not sure about your car, but those can be a real pain to get to in some cars. You could try bypassing the heater core; generally there'll be two hoses passing through the firewall and you'd just disconnect both of them and use a piece of pipe to join them together with hose clamps. That should stop the leaks and will help diagnose if the leaking heater has anything to do with your overheating problem.

Frankly I'm skeptical about the fuel pump diagnosis; unfortunately you'd have to have a pressure gauge to tell for sure.