a week ago is the perfect translation for this locution. but your others translations for il y a quelque chose are also correct.

Literally, il y a means there is or there are (the difference between singular/plural comes from the following indefinite article / number / indefinite adjective or pronoun (the three forms exists and have the same meaning there is a quantity of something), in that case il y a un problème for singular and il y a des problèmes for plural

However, the definition of the locution change when the sentence is a matter of time. Talking about time, il y a refers to a past time period, specified by the following : il y a une semaine is a week ago because it’s exactly a period in the past a week far from now

This is a correct translation, il y a + a period of time is a very common and standard phrasing. You can use it with any other period of time: il y a cinq minutes, il y a deux ans, il y a un mois, il y a cinq millions d’années, il y a cinq siècles, etc. You can also use with less specific spans of time: il y a quelque temps, il y a un bout de temps mean some time ago, or il n’y a pas longtemps means not long ago. Il y a peu is a bit more formal, and is an idiom for a short time ago.