All Finnair award flights come with baggage allowance. Economy awards have 1 bag included and business awards have 2 bags. Normal Oneworld rules apply, so Sapphire or Emerald even gets you one extra bag. Both shorthaul and longhaul are the same.

It shouldn't matter which airline miles are used to buy the ticket. My experience is from using BA Avios but I have always had the above bag allowance included.