Where do I sell Firewood in Riften for 5 Coins/Firewood?
Is there someone in Riften who take orders? or do I need to sell it at a Farm outside?

Usually its the innkeepers that will buy it off of you so try the Bee and Barb

She doesn't accept them.

Don't see any buyers in Riftin, but outside at Heartwood Mill there should be one unless a dragon ate it.