It's the same rules as before, with additional tighter rules for diamond elo, with the stricter rules coming into play if both apply.
Plat 5 would normally be able to duo with a diamond 5, but diamonds can only queue to within 2 divisions, and so a plat 5 can't duo with a diamond 5. The diamond 5 can duo with plat 2 or plat 1, but nothing lower.
A plat 5 can duo with anyone in gold, as the within 1 tier rule applies.
Lower than gold (i.e. silvers and bronze) can't ever be in a premade with a plat ranked player for ranked games.
The limit only applies to ranked queues, you can have a premade with whoever in normals.
A bronze 5 can't currently premade with a gold 1, only other bronzes/silvers due to the 1 tier rule.
Unranked players who have never played ranked before are considered silver for the purposes of premade allowances (so they can be in a premade with anyone from bronze, anyone from silver, and anyone from gold, but no plat+ players). If they've previously played rank, their final rank from last season is used.
Ones final rank from last season is considered only in so far as who they can be in a premade with during their placement matches (i.e. their first 10 matches). So if you were plat 1 at the end of last season, you could duo with a diamond 4 for your 10 placement matches, but then after you were placed you would have the rules that apply according to where you were placed. So if you then placed gold 3, you would no longer be able to duo with your diamond friend until you climbed back up to your high plat rank.