Learn Spanish (Spain): Mi abuela vive en una residencia desde el año pasado. - My grandmother has lived in a nursing home since last year.

In Spanish, when an action started in the past and is still happening right now, you use the present tense along with a time marker like desde (since). English uses the present perfect, but if you said ha vivido here, it would sound like the action is finished or you are focusing only on the past experience rather than her ongoing living situation.

Why does una residencia translate to a nursing home instead of a residence?

While residencia can mean a generic place of residence, in everyday Spanish it is the common shorthand for una residencia de ancianos (a retirement home or nursing home). Using it by itself in this context makes it perfectly clear to a native speaker where the grandmother lives.

Could I use desde hace instead of desde in this sentence?

Not with el año pasado. You use desde for a specific starting point in time, such as a date or a specific year. You use desde hace when talking about an amount of time or duration, like saying desde hace un año (for a year). Since el año pasado is a fixed point in time, desde is the correct choice here.

Why isn't there an extra preposition like en before el año pasado?