1. Yes, its normal for a heaters to not heat to the exact temperture you set it to. Adjust the temperature setting until you get the water at the temperature you want. If you need to set it to 28 to get a water temperature of 24 thats not a problem.
2. Depends on how good the thermastat is on the heater. Ive had heaters that kept the water consistent. Ive had heaters that allow the temperature to drop a degree or 2 overnight when its cold, and then warm up again during the day as the heating comes on. Never caused me a problem but it depends on how much that temperature range is. 3 degrees C might be a bit much.
What you see might be an issue with not having enough flow around the heater. You want the water to warm up and dissipate around the tank. If its just warming up the water around the heater and then not circulating, the water temperature around the tank wont get the benefit and you will see these temperature fluctuations when the room temperature drops. I like the heater next to the filter intake so that the water warms up as it enters the filter and the filter output circulates that water throughout the tank.
Another issue is 150W is a big heater for 70 litres. You typically want 1W/litre plus a little bit. So a 75W heater is good for 70 litres. 100W if your room temperature is particularly low so it has the power to raise the water temperature that little bit more.
An oversized heater will heat the water quicker then turn off, coming back on when the temperature drops. So its constantly turning on and off. The heating element wont be on so much so this preserves the heating element, but the thermostat/ switch will wear out quicker because its turning on/ off more often.
An undersized heater will take longer to heat the water, so the heating element is on more and will wear quicker, but the thermostat/ switch will be preserved as its not turning on/ off as often.
You will find advocates of both using oversized and undersized heaters, but IMO
having the right size heater is best.
Another issue with an oversized heater is if the thermostat/ switch fails in the "on" position it will more quickly heat up the water and you could overheat your fish before you notice a problem.
You ask do you need to get a "new" heater. Did you buy your aquariun set up used? Ive never had a heater last much more than a couple of years, so if its a used heater i would probably replace it as it might not last much longer anyway depending on how old it is.
What brand heater is it?