I presume the house has had electricity at some point as it has light fittings and switches etc.
Not necessarily mains – there could have been a generator or a solar panel and battery for that small a property. Has there been a meter there at any point? Is there a supply cable? It would be unusual for a mains electricity supply to be done away with completely – it’s usually disconnected at the meter.
I also believe the property would have to be completely demolished to go up, due to its foundation being too shallow.
Not necessarily – you would need to carry out a spot of site investigation to expose the existing foundations and find what they are sitting on. Best to get an engineer or architect to take a look and give you their professional opinion. If there is scope it is sometimes possible to underpin the existing foundations to take additional load. However, this can work out just as expensive as demolishing and rebuilding especially if there are internal walls involved too.