I was contacted by R. Leib Tropper, who presented at the recent EJF conference discussed in this post, and he offered the following clarifications (in my words, which he approved):
1. R. Tropper does not believe that R. Eisenstein said in the name of Rav Elyashiv that someone who believes that the world is older than 6,000 years is a heretic. Rather, he is not worthy of being a dayan. Presumably, this means that the past conversions he performed are still valid.
2. R. Tropper quoted Rav Chaim Kanievsky as saying that a person who believes that the Sages of the Talmud could have made mistakes should not be converted. He does not rule definitively on someone with that view who already converted.
3. R. Tropper stated that dayanim should dress conservatively and that even secular courts have dress codes. However, he did not state that dayanim who do not dress appropriately are disqualified from serving as dayanim.
4. R. Tropper also said from the podium that it is the opinion of R. Elyashiv and R. David Feinstein that a Beis Din performing a conversion should release the "Te'udah" (certificate) immediately so that the convert can move on.
1 & 2. It is impossible to have truly universal standards for conversion (and dayanim) because the standards of different communities are contradictory and, even if not, would be incredibly restrictive. For example, the Satmar community would demand that Zionists cannot be dayanim because they are heretics. I do not know how literally they take this, but the Satmar Rav wrote that anyone who votes in an Israeli election has the halakhic status of an idolator and, presumbly, is disqualified from serving as a dayan. On the other side, there are communities that follow the rulings of the Rambam and Maharal that those who pray to angels or human beings (including rebbes) are heretics. Should we disqualify from serving as a dayan anyone who is a Zionist or recites "makhnisei rachamim"? I don't see how that is possible. If you are a follower of Satmar or of an ultra-Rationalist, then you must follow those rulings and disqualify as dayanim as above. But if that is the case, then you should not be trying to institute "universal" standards that exclude large segments of the current Orthodox community.
If (and I stress IF) Rav Elyashiv holds that the majority of Orthodox rabbis in the US--including the most active dayanim in America who oversee hundreds of gittin and conversions a year--are disqualified for serving as dayanim, then his followers must abide by that ruling. But I don't see how they can impose that on the general community or claim that by following him they are implementing standards that are anywhere near universal. As above, truly universal standards are impossible. Close-to-universal standards would be as inclusive as possible, not incredibly divisive and exclusive.
3. I think every rabbi and dayan agrees that dayanim should dress appropriately. The question is what is considered appropriate, and on this standards differ based on time and place. No one would require dayanim to dress the way dayanim in Rambam's Egypt dressed, nor in Rav Ashi's Bavel. Therefore, I don't know that an out-of-town rabbi should need to dress according to Boro Park fashion, nor should a Boro Park dayan need to dress according to Wall Street fashion. Colored shirts and wedding bands may raise eyebrows in Monsey but in Teaneck they are considerable respectable, formal and wholly appropriate.
4. Nothing to add.