"Where did you live last year?"
Translation:Var bodde du förra året?
Sorry! I read that too quickly. :)
No, they're not synonymous - sista means last as in the final one, but förra means last as in the previous one. So I should have been clearer: you can use sista året in other sentences but it doesn't work here.
You can absolutely say sista for plurals as well. For instance, (de) sista åren.
Would it be possible to use a preposition before förra året, e.g. "var bodde du i förra året", eller, "...under förra året".
If it is possible does it change the meaning at all, I am imagining that it may be the difference between where were you living a year ago and for the last year.