Categorical, nominal or continuous variable? I'm trying to understand what level of measurement is best for describing the 'number of rooms in a flat' feature.

First of all, I think it's not a continuous feature, because rational values like 1.42, for example, don't make sense.

To decide whether a feature is categorical or nominal, we should try to find an ordering between values. And here is my question: should we look for an order with respect to the response feature (in my case 'Price of a property')?

We can say a '1-room flat' is cheaper than a '2-room flat', and so on. But that is not always the case. In general, maybe it's true, but there are cases when a '1-room flat' in the city centre is way more expensive than the one further away.

So, a can't decide which representation to choose - categorical or nominal.
I don’t know where you’re getting this particular classification scheme from, (continuous, categorical, nominal), but it’s worth mentioning that this isn’t a great scheme for classifying data types. You’ve already encountered an example of a data type (count data/natural numbers) that doesn’t fit neatly into them.

It is also worth mentioning that a lot of people will use “nominal” and “categorical” interchangeably to describe a discrete data type with no natural ordering. Probably the most widely-accepted term to describe discrete data with a natural ordering is ordinal data.

In this case, "number of rooms in a flat" has an unambiguous ordering. In a very real and intuitive sense, a five-room flat has more rooms than a two-room flat. A one-room flat has fewer rooms than a three-room flat. It makes sense to talk about one flat having a greater or lesser number of rooms than another, and if we want to know if that ordering matters in some way, we need to preserve the ordering in our analysis.