I am sorry for your situation. To be very honest with you, there is no way this can be construed as fraud or deception per se, given that the marriage took place. If it had not taken place, then you might have been able to do so, but once the marriage took place, your agreement to it supersedes any problems before it. Furthermore, it can also be said that you having received residence rights in Germany is also a benefit of this marriage, so the benefits were not one-sided.
On the other hand, my suggestion would be to fight with her on the divorce camp. First of all, let me ask you if you are sure she is filing for annulment or divorce. These are two very different situations, and the conditions are also very different. If it is indeed annulment, then your chances of receiving back the engagement ring are quite high, because annulment means 'reverting to the original state' as if the marriage never took place at all, and therefore any marriage gifts must in principle be returned. However, annulment usually has very strict conditions, such as:
- the parties not being of age, or being already married;
- the purpose of the wedding being to defraud the state (which, if she claims so, would put your residence in jeopardy);
- the marriage was invalid as to its celebration (which I do not think is realistic).
I am much more inclined to think she is actually suing for divorce. In this case, the country where she must apply is Germany, because that is where your last common habitual residence was. If she files in Romania, you may, by hiring a local attorney, deny the jurisdiction of the Romanian courts. The law to be applied is also that of the last common habitual residence, i.e. German law (unless you had a marriage contract whereby you chose Danish or another law as the law applicable to your marriage).
In a divorce proceeding in Germany, you may try and claim back the engagement ring by showing how the marriage lacked substance (she did not tell about it, the purpose for her was to get your money etc.). If you wish to claim deception, you may also do so as a counter-claim to the German trial.
Please note, to make it very clear, that nothing from your question even raises the possibility of a criminal issue. Everything falls within the civil laws, and therefore the proper terminology is 'claim' and 'counter-claim', and not 'prosecution'. Romanian laws, for one, do not know of a crime similar to the circumstances you exposed so even if you would manage to find a country where what she did is punished criminally, the Romanian justice system would not recognize such a decision.
I hope my answer was clarifying and look forward to your further questions or to your rating, which is essential to my activity.
Dr I L Vlad