Is it a free-standing oven? Vaguely recall you mentioning that. They can be gas only, electric only or dual fuel (electric oven, gas hob). I think gas ovens still use the 'gas mark' system rather than having the oven temperature marked in degrees, so that will be a clue. Gas ovens are pretty crap, gas hobs obviously good. Hence the appeal of a dual fuel thing...
Personally prefer fitted appliances. The oven will usually be fixed into a cabinet beneath the hob... The hob will be mounted in the worktop. Neater. And it gives more flexibility in terms of appliance choice... e.g I have quite a wide 5-ring hob mounted over a standard sized oven. However reconfiguring your kitchen can get bloody expensive, so probably best working with what you've got.
You can of course just ask if there's gas. But if they don't know there are clues - boiler will generally be gas, but if the hot water is a cylinder it's probably electric. If there are plumbed-in radiators, probably also gas... This is because gas is cheaper per KWh, so effectively the system just heats water and pumps it round. Electric heating systems will produce heat directly - more efficient. That fake fire is electric, but could just be a later addition.
If you need any advice on kitchens etc, feel free to get in touch... It's not really what I do, but I have fitted a couple. The guys above my workshop do a lot more of that kind of thing, but we're all kind of on the expensive end of things.