How should I translate "Made in Rome" and "Made in 2022" in latin.
What you typically see on inscriptions is the person who made it, me, and fecit. People took ownership of their craft back then, as opposed to mass produced things today.
But since presumably you don't who the person who crafted your object, we can use the passive, which would be factus, -a, -um est. For example, "this thing was made" equates to Hoc factum est. (See for example this manuscript).
Denoting the year is as simple as writing anno (ablative of annus meaning "year") followed by the year in Roman numerals. So Hoc anno MMXXII factum est.*
For location, you do have more options, but generally for countries you'll simply use in plus the ablative. With Rome in particular (and other cities) you'll have to use the locative, Romae.
Hoc Romae anno MMXXII factum est.
This thing was made at Rome in 2022.