If I marry a US citizen in the EU and we live in the EU for 2 years and then I apply for a green card, will it expire after 2 years?

No. If you have been married more than 2 years when her case is approved, then her card will be good for 10 years.

If you are married for more than 2 years at the time of your interview for the green card/immigrant visa, if you are granted the permanent resident status, it will not be conditional but will be a permanent card.  Please note, however, that after applying for an immigrant visa, it will take about 9-12 months to go through the process before the interview, so it is not just a matter of applying and going right to the US.  You might, therefore, plan accordingly.