With option 2, you can definitely forget about the house. With your savings rate, you will never keep up with the price increases.
An owner-occupied apartment (ETW) would definitely be an alternative for me in your position. I still can't imagine your house construction happening in 3 years without significant income increases. With a €600 payment, you would only have €16k equity in 3 years, which is better than now but not great yet. At least the private loans would be gone. I still haven't quite understood why only a €600 payment is possible, but with private loans, rent, and only parental allowance left, it will probably turn out that way.
We save between €3000 and €4000 monthly with comparable income, and so over 2 years with a variable loan, we reduced the outstanding debt by €85,000. That obviously made the whole undertaking much easier. But firstly, for example, we live rent-free, so you can't really compare it with your situation, and secondly, even where we live, many people still find it extremely tight or too tight.
But as you and some others have already noticed, buying land would not be a significant risk. You can simply sell it again in 3 years with a profit/no loss if building doesn’t work out.