What exactly is permitted on Shabbos, when buying a house in Eretz Yisrael?

The gemora in Gittin 8b says that even though one is rabbinically prohibited to tell a gentile to violate an issur on Shabbos, nevertheless, when it comes to buying a house in Eretz Yisrael it is permitted. The case involved in the gemora concerns the person who had already purchased a house from a gentile, but the deed had not yet been certified in court. The gemora says that since it involves the mitzvah of yishuv Eretz Yisrael (settling the land of Israel) one may instruct a gentile to draw up the contract and have it certified in a gentile court. The only prohibition involved is 'amira l'akum'  (instructing a gentile) which may be waived in face of the mitzvah of yishuv Eretz Yisrael.

I have heard though that much more is permitted when it concerns the purchase of a house in Eretz Yisrael?

It is a fallacy. The Mechaber [1] says that one may purchase a house from a gentile in Eretz Yisrael and have the deed signed and certified in court. The Mishna Berura [2] explains that one may direct the gentile to where the Jew’s money is and the gentile can sign and certify the sale but the Jew may not handle the money and give it to the gentile.

We see that even though handling money is only an issur of muktze, nevertheless one may not handle money in order to make the purchase.

But is the writing not an issur d’oraisso (biblical)?

Indeed it is, but since it is not the Jew who is doing the writing but rather the gentile it is permitted. This is one of the unique cases where we may instruct a gentile to violate an issur d’oraisso, as explained in the Mishna Berura. [3]

Is every purchase in Eretz Yisrael called yishuv Eretz Yisrael?

It is not so simple. Rashi in Gittin says that the mitzvah is to relocate the gentiles from the land and settle Jews in their place. The Mechaber also writes “One may purchase a house from a gentile”. This would mean that to buy a house from a Jew in Eretz Yisrael does not fall into this category. This does not demote the actual residing in Eretz Yisrael, which according to the Rambam is a Mitzvas Aseh, but buying a house from a Jew (according to these poskim) will not allow the instructing of a gentile to do anything.

When is one permitted to violate the Shabbos in order to prevent a fellow Jew from doing a greater sin?

In the yesteryear ovens, bread dough was pasted on the side of the oven and removed with a special spatula. The halacha is that it is ossur to use this spatula on Shabbos being that it is an ovda d'chol'. [4] The Shulchan Aruch [5] talks about a case where someone pasted dough inside an oven with the deliberate intention of baking the dough, and says that he is permitted to peel the bread from the oven (even though an issur is being violated by doing so). This was permitted in order not to create a much more severe issur of baking the bread.

The Mishna Berura [6] says that only the baker who pasted the bread in the oven may remove it and not someone else, even though the intention is to prevent the baker from violating a very severe issur. Peeling the bread is an issur and we do not say that one should violate even a small issur in order to prevent another person from violating an issur, even though it is a more severe issur.

What if the person pasting the bread is unaware that it is an ossur - for instance, he thought it was not yet Shabbos. May I remove it from the oven?

The Mishna Berura says [7] that the same halacha applies when the person pasting the bread is unaware that he is violating an issur. The Magen Avraham explains [8] this applies even when it is done unknowingly. As there is an element of carelessness involved, as one should have taken more care, one may not violate an issur for the sake of another person.