Is it worth buying short term links? Like month, 2 months.. Or it is only worth getting links permanently or at least for a year?
You have to be quite careful with paid links since they are against Google's terms and conditions. That being said, I'd say the longer the term the better. Search engines can see when a link is removed. So once it is removed you may very well lose those benefits. If your site develops a trend of losing a lot of links regularly it could look quite suspicious to Google.
Ofcourse permanent link ! building shorterm backlink is just waste of time because you will not know that when google crawl your site and backlink and you dun know when is the google update. Forget about building shorten backlink, focus on permanent backlink will do .