It all looks a bit similar to what we have.
I also think it's definitely doable.
It already comes across that you know how to save. You're doing everything well!
Set the house budget more around 350k, if that's even enough... At the beginning, we also looked into prefab houses like Schwörerhaus, Weberhaus, Hanse Haus, Haas, etc., had 130-140m² houses, and all in all, we never came out under 400k! So definitely watch out there. The follow-up costs with prefab house providers are also much higher. With a double garage, I think even 350k is hard to manage. However, my offers are based in BaWü, where everything is naturally a bit more expensive.
I would budget the kitchen rather at 15k instead of 10k.
Don't forget the outdoor facilities! With some own effort, you're quickly at 10-15k there.
Don't forget the general ancillary building costs. These quickly amount to about 50k for a single-family home. You didn't list those in your post.
I would definitely put aside about 10-15k of the 50k equity for unforeseen expenses and for the future.
If you can pay for the plot in cash, then do it. We got a variable interest rate for 1 year of 0.82% and according to the bank's calculation, we had interest costs of just under 800€ for 1 year yesterday. Which is really okay. The question would then be whether you should save the money for your house loan to get better interest rates there? It's just a calculation matter and hard to say beforehand, you have to talk to the bank.
I would save the money for the furniture together in the interest-free year at the beginning. You are already putting away 1500€ now --> times about 12 months makes 18,000€. So that adds up a bit.
1200€ repayment could be realistic, we are currently at just under 1600€, but we also have a bit more loan set, which could still come for you depending on the house costs. So 1200€ could be tight. It should at least be paid off by retirement age; for us, it works very well with 1600€ and just under 2.3% repayment. You would have to discuss that with the bank.
Ah, I completely forgot: Are you building with a basement or without? This might mean that the house costs are not quite as high as I estimated.