1-That’s right, it’s mileil on the syllable hav. The vav must be a vav not a melupam/shuruk because the hey already has a nekuda.
2-No, and the English translation is stilted and frankly not that great, but the Hebrew side is very meduyak in girsa, based mostly on R’ Yaakov Emden. And that was a misleading typo, it should have said “I’ll” say rather than “I” say as in I should say. To be honest, I don’t watch the dikduk much while I’m saying korbanos and just say “bar kapara” like we do in learning. Sorry.
3-Once again, you’re right. it’s yacheyd. Yachada is Chabad-ari.
4-Of course it’s muttar to say havaya, but I don’t think that’s what the nussach says. All l’shem yichuds are based on the Ari. The basic idea (very basic) is that mitzvos “reunite” the two halves of Hashem’s name — the yud-hey and the vav-hey in a “yichuda shlim” — complete unification and we are declaring our intent to make the combination through the mitzva we are about to do.