Construction in outdoor areas (agricultural operation)

Hello,
my girlfriend and I (both 25) are slowly starting to plan the construction of our house. I have a few questions about this and hope someone here might be able to help me.

So I'll start from the beginning: girlfriend, 25, full-time childcare worker, me 25, I work in my father's agricultural contracting business, which I will probably join in the next few years. At the moment, I am still doing further training to become an agricultural service manager, which will be completed in March next year. We currently live together in a rented apartment. Equity at the moment about 25,000 (increasing by about €1,500 per month). Net income about €4,000.
Planned is the construction of a single-family house with an attached garage. What we would do ourselves: soil replacement etc. (with our own machines), complete garden, construction of the garage,
Here maybe a brief assessment from your side regarding the financial situation

Now to the actual topic. Our dream would be to build on my father's agricultural property. The only problem is that it is located outside the designated building area [Außenbereich]. Agriculture and an agricultural contracting business [landwirtschaftliches Lohnunternehmen (Gewerbebetrieb)] are operated there. My parents, my brother, and my grandmother currently live on the farm. Our house should stand about 30m next to the other house in a pasture. The rest of the pasture would remain. In short, there is enough space, the only problem is the permit. Maybe someone has experience with this or can help.

The second option would be, if this is absolutely not feasible, to buy a plot of land in the village (about €30,000 - €35,000) and build there.

If there are any questions, feel free to ask.

You as a son will be allowed to build there. Has anyone refused that? I don't think so.

No, nobody has rejected it so far because no one has asked anywhere yet. However, many/all of those I have talked to about it so far have said that getting the approval is not that easy because it is located in an outdoor area.

But it is your company. You have special rights if you continue it.

But it is your operation. You have special rights if you continue it.

I am rather skeptical about that. Special rules for building in the outskirts for farmers exist in my opinion only for operational facilities – not for residential houses. But maybe knows more if he drops by.

Go to the municipality and ask. Based on the mentioned property price, I assume you live in a rural area far away from densely populated regions. In that case, [Kuhkaff] could actually be an advantage. People in [Kuhkäff] usually want young families to stay.