When it 'feels like it wants to die', how fast is it running? Slowing down when coming to a stop, the fuel injection is actually shut off most of the time. Just before you stop, it turns back on to keep the engine running. You might be feeling this if you are slowing down in gear with clutch out.
If in neutral or clutch in....I'm not knowing for sure as it should be idling although some will idle a bit higher until you actually stop. Being a 4 cylinder engine, it is normal to feel it shake a bit at low rpm...especially if you have some miles on it. The engine mounts tend to get firmer as they get older so you feel more shaking with old mounts than new ones. This is assuming that the mounts are all in good shape and you don't have a broken one...which can cause some shaking for sure.
Fuel filter is in the tank...don't worry about it. I'm not super happy with the stock spark plugs they put in the engine. Mine didn't run good at all until I put better plugs in it.
How is the gas mileage? That is the best way to determine if the engine is healthy or not. If your mileage is normal, and the engine runs well except for the shake at idle, look at mounts or something external for the cause.