Tragically, an immediate family member who is secular has decided to marry in Cyprus to avoid the rabbanut. I will try my best to persuade the opposite (even though that seems more impossible now with the closing of Tzohar). In the event that my efforts are unsuccessful and the member does get "married" there, I am unsure as to how to approach them afterwards.
1) Can I congratulate and/or give them a present? How do I treat the subject?
2) They are having a celebration party in Israel once they return from the trip. They have asked me, as a sibling, to play a role in the planning/speaking of the event. Is this forbidden?
3) Is a civil union of two Jews in Cyprus accepted halakhically as a b’dievad proof of marriage (I’m thinking of Rav Feinstein’s teshuvah on the issue)?
Thank you and shalom.
In dealing with questions of this type, a lot depends on the unique situation of each case. For example, what is the relationship you have with the couple, what are their feelings about Torah and Mitzvot, etc. But I will try nonetheless to give some broad answers that may help you in finding the best path to take in this case.
I am assuming that the couple is one that is halachically allowed to marry each other - that is two Jews, without any problems to do with forbidden Cohanic marriages, or pending divorce issues that would create halachic problems. If there are halachic problems in the marriage itself, and not just the fact that they have decided against a religious Jewish wedding ceremony, then your problem is much more serious, and I would have to deal with it in a separate answer after hearing more details.
This being the case, the sin involved is twofold. Firstly, they are going to live together as man and wife without "chuppah and kiddushin", which is itself forbidden. (Though - and I hope that I am jumping to wrong conclusions here - they may well be doing that already without any ceremony in Cyprus or anywhere else!). The second problem is a much larger one. It may be that by making such a statement, they are trying to divorce themselves from Judaism, the Jewish people and its Torah. This is a very serious sin and problem in itself.
Without knowing the couple it is hard to give good advice - but usually we are talking about people who have very little connection to true Judaism. If this is so, my feeling is that it is incumbent upon us to do all we can to draw them closer, whilst still retaining our own integrity and honesty to our own beliefs.
So, I would not directly congratulate them on going to Cyprus and getting"married" - but I would give them a gift for their new home (perhaps a mezuzah or chanukiah). The distinction is that you are not directly condoning their act of rejecting a traditional wedding, but are making an effort to keep good relations with them. After all, you really do want their new house to have blessings (and a mezuzah or chanukiah). A blessing such as "I wish you all the best for your new home", "may you both have only blessings", or "You two are always in my prayers - may you be granted a great life together" is also in order.
About participating in the party - this is a very sensitive issue that really only you can answer. The main thing to consider is: what will you gain by refusing to take part as opposed to taking part? Will your participation be seen as giving approval to their act of sin? Or will it be seen as maintaining good relations and acting like a "mentsch" and hoping that they may one day have a stronger connection to Torah? I assume they know of your disapproval - so will your involvement at the party perhaps give it a more "Jewish flavor? Will that make it kosher? Not with Shabbat desecration? More "tzanua"? On a technical level, if the party is one that celebrates the "marriage" in Cyprus, it is problematic to be involved as you are supporting an act of sin [though from a purely technical halachic perspective one can find ways to allow it]. For example, we would not approve of going to a party celebrating a successful bank robbery. If, however, it is to celebrate that two Jews have decided to dedicate themselves to each other and build a home together, it is allowed. The fact that they did not do a chuppah, (or go to the mikvah, or put tefillin on that morning) does not detract from the fact that what they are doing is a good thing - i.e. a couple committing to build a home based on love and affection, care and concern for each other. This is an idea we would like to strengthen. So the decision lies with your judgment - may you be granted the wisdom to decide correctly. You may want to consult with a rabbi who knows you and the couple personally, as they will more likely be able to direct you in a clearer fashion.
In connection to your question as to whether this would be considered a halachic marriage - this is a matter of debate between the poskim. But both sides would still say that it was a sin not to have done "chuppah and kiddushin" - the only question is whether they would need a divorce if they broke up. My (limited) understanding is that today the Bet Din would try to get a divorce issued if they did break up, but would rely on the lenient opinions if unable to do so (or if there was a question of mamzerim). Of course this is really an issue that a qualified Bet Din would deal with.