(1) Why is the mizbeakh an issue since the korban pesakh wasn’t brought on the mizbeakh? (2) Is it true that a yisrael could schecht the korban pesakh if there was no kohen? If so, why do we care about yikhus and bigde k’huna? Speaking of which, why are bigde k’huna or t’khelet etc. m’akev? Why does R’ Kalisher think we should dye it blue instead of leaving it blank like tsitsit (assuming they haven’t rediscovered t’khelet again as I am discovering many mainstream American kharedi rabbis who tuck their tsitsit in are deciding)? (3) How have R’ Steinsaltz etc. resolved these issues—like R’ Kalisher?
ב"ה Shalom The issue of bringing a korban pessach in our time can fill treatises which are not within the scope of this forum in which we try to give concise answers to the many people who turn to this site. I will therefore focus only on your first question in regard to the mizbeach. The pessach had to be brought in the proximity of the mizbeach, therefore knowing it's place is crucial in bringing the Korban Pessach. (See משפט כהן סי' צא). According to Rav Tzvi Pessach Frank zt"l, ((ספר מקדש מלך, ושו"ת הר צבי יו"ד, עבודת בית הבחירה בזה"ז סי' יא). , one of the reasons the korban pessach cannot be brought in our time is because no korban can be brought without the korban tamid on the mizbeach first and since the tomid was bought by the shekalim which are collected only when the Bet Hamikdash is standing, there is no possibility to bring the korban pessach unless the Bet Hamikdash is built and the Shekalim collected. You will have to speak to Rav Shteinzaltz in regard to his opinion on the matter. All the best