"This is a shoe."
Translation:To jest but.
Yes, you're quite right. Simple sentences of the "This is an X"/"These are Y" form take Nominative (and also alwas "to", treated as the subject and not a demonstrative pronoun), defining a noun with another noun takes Instrumental.
"Ten" means "this" but as a determiner describing the noun (in Polish specifically masculine). Not as a standalone pronoun which indicates a nearby object - to this meaning corresponds Polish "to".
"Ten" can be also used in sense "this one" (masculine noun).
You can, it's accepted, but I wouldn't recommend it. On its own, as a super-short sentence, it seems clumsy to me. Also, it's not like "ono to but", because "ono" is really rarely used at all. All constructions like "This/That is X", "These/Those are X", use impersonal "to" as the subject, regardless of the grammatical gender.