(Bamidbar 7:16) "One he-goat for a sin-offering": to atone for (defilement by a "grave in the depths," (i.e., unknown tumah). "And for the sacrifice of the peace-offerings": From (Ibid. 88) "And all the cattle for the sacrifice of the peace-offerings," I might think that "cattle," where it is explicitly stated, are valid for peace-offerings, but not the others; it is, therefore, written "And for the sacrifice of the peace-offerings," to indicate that all are valid for the sacrifice of peace-offerings.
"This is the offering of Nachshon ben Aminadav": He brings his own and not his tribe's. "this is the offering": This one (the chief, in the inauguration of the altar) brings donative incense, but an individual (as opposed to a congregation) does not (otherwise) bring donative incense. "this is the offering": This one brings a sin-offering, not for a sin, but an individual does not bring a sin-offering not for a sin. (The offering of) this one overrides the Sabbath and tumah, but an individual does not override Sabbath and tumah.