How to proceed correctly? Some confusion/time pressure

The very cheap price would also make me very suspicious. No one gives anything away for free. Have you asked the owner directly why he set this price? I wouldn't rely 100% on the truthfulness, but you can already read something from the reaction.

The city/municipality states here that the land price averages 250€/sqm. So that would fit. However, since we have already rejected other plots available here with prices of 350-400€, which are still being sold, we are initially cautious.

Sign the purchase contract (if it is your dream property) and date the handover and payment to, for example, December 19th :)

That was not known to me, I thought the purchase contract is signed at the notary and not beforehand. But that means I then have to make the payment (or instruct the bank to do so) + real estate transfer tax, and then the purchase is completed?

We have already been able to clarify a few questions. There is no easement on the property and otherwise everything seems to be in order. Next week we will meet the owners in person to clarify the details (price, date, etc.).

You can specify exactly in the [Notarvertrag] when payment and/or transfer should take place; these can also be dates several months in the future. However, your contractual partner must agree to this.

As lastdrop says: a date is entered in a notary contract. This is rarely dated as immediate, since there is still a lot to arrange. In this respect, one can remain calm and take the end or also the beginning of next year. Three months are not uncommon. You are not the owner from the notary appointment, but from the date that is stated in the contract.