Can a 7000 watts generator power a house?

A 7000 watt generator us typically intended for 2 - 15 or 20 amp circuits at 120 volts or 1 - 30 amp circuit at 240 volts. When you say, "power a house," if you mean the whole house the answer is, No. You would need a generator capable of supplying a continuous 24000 watts or more to do that.

But a 7000 watt generator is a nice one for powering some lights and your gas furnace blower during a power outage when properly connected.

I do not know what the wattage is of an electric furnace to know if it can run one of those.