How rental income is considered in financing

Hello,
I am new here and have two questions right away.

1.
We plan to largely finance our construction project through rental income from a fully paid-off, almost new apartment in a prime location in Karlsruhe. The cold rent is expected to be about 1400-1500 euros per month.

I am currently the sole earner with about 3000 net. We have about 300,000 as equity with an expected construction sum of 700,000-750,000. The plan is for an architect-designed house with about 200-230 m² of living space, 3 stories without a basement.
The land costs amount to 310,000.

We already went to the Sparkasse on site for land reservation and roughly calculated this with these key data, concluding that the construction project is feasible this way.

However, I have often read that rental income is sometimes not taken into account in a financing request.

Has anyone of you had experience with this?

2.
I always read here about construction costs of 1700-2000 euros/m². On the other hand, a colleague of my father, who is a builder himself, said that the costs are calculated in euros/m³. As a concrete number, he mentioned about 350 euros/m³ for a turnkey house with normal equipment.
So what is correct now?

Many thanks!

Regarding 2: both are correct, they are just two different approaches

1) The rental income should be considered (less service charges and other reserve formations (e.g., 20%) and taxes).

Thank you for the answers.
Do you think the financing is feasible so far? The example is currently the worst case, as my wife will go back to working part-time after parental leave and then an additional approx. 1000 euros per month would come in.

If I now take, for example, a cuboid with 10*10*10 m. According to the calculation, I would come to about 350,000.
I would then have more than 250m² of living space, right?
If I calculate 250*1800, I come to 450,000.
Where is the flaw in my thinking?

I believe that 350 euros in volume is a relatively low value, but 1,800 euros per area is already higher. For our "affordable" house in volume without an attic (but with a basement), I come to about 385 euros, with an attic about 340 euros.

Due to the crediting of rental income: Depending on the condition of the property and its rental suitability, my (employer's) bank deducts between 10% and 20% from the cold rent. The cold rent is the lower amount between the information provided by the (future) landlord and my own market research. So, if you say you have a concrete tenant who pays you €10/sqm and according to market research/internal database you only get €9, then €9 would be applied (minus 10-20%, as described).