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.
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7 kw = 7000 w 7000 w / 220 v = 31,818 A Answer is 32 A MCB
AC depends on a lot of things. It's not as simple as you think. It depends on ceiling height. Sun exposure. Your climate. And part of the cost may include a crane to get air handlers up on the roof. You should consult with some reputable commerical HVAC dealers in your area to create a good workable solution. AC isn't cheap. The unit for my 1400 sqaure foot house with 9' ceilings is about $7000 and I still have to run the duct work.