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A bull-calf (a two year old calf).
Because Hashem was going to "appear" before them on that day.
Nadav & Abihu.
Because they offered strange fire before Hashem which he had not commanded; also some say they had been drinking.
That Aaron should not grieve; that through those close to Him (the priests), Hashem would be sanctified and glorified; when those close to Him do not follow His instructions exactly, they are subject to the maximum penalty; sets the wrong example for the people.
Because they were Cohanim, had been purified through the 7 days, and would be defiled by touching dead bodies.
Eleazar and Ithamar.
Because they did not eat the sin offering in the place of the sanctuary as commanded, and the blood was not brought into the sanctuary as commanded.
Aaron explained that it would not have been pleasing to Hashem if he (they) had eaten the sin-offering after what had happened to him (them) on that day.
Chew their cud; parted and cloven hoof.
Until evening and after he and his clothes are thoroughly washed.