Timber wasn't that valuable, especially as the cost of moving it from North America to Europe would have blow its price out of all reasonable proportion. Timber was valuable to those living in Greenland due to the scarcity of trees there, but much of the rest of Europe instead used managed woodlands to provide the timber they needed.

So there are two accounts of Leif Erikson's story: Saga of Erik the Red, and Saga of the Greenlanders.

Saga of Erik the Red says he was blown off course on his way to Greenland from Norway. He landed in Vinland, and found grapes, wheat, and maple trees. He eventually loaded the ship and went back to Greenland. He never went back, but others did.

Saga of the Greenlanders is different. Bjarni Herjólfsson was the first to see America, spotting it but not disembarking. He returned back home to tell about his discovery, and Leif decided to buy his ship so he could go back and explore. He eventually made it to Vinland, meaning Wineland because of all the grapes there. He stayed through the winter before leaving in spring or summer. Again, he didn't come back, but people such as Thorfinn Karlsefni made settlements.

They just took a bunch of resources and left, and they did have wood. They really didn’t have the need to do it. Also, part of the reason why they left is because of trouble with the natives.

I hope this answers your first question, but it’s mostly copied from a previous comment I made on a different question.

It's not known if L'Anse Aux Meadows was their only settlement in North America. From the descriptions of Vinland it seems likely that they explored the Gulf of Saint Lawrence. They might have gone further, we don't know.

Timber was very valuable to the Greenland settlements, but not valuable enough where you would export it to Europe. Vinland wasn't barren of forests. Perhaps you're thinking of Markland (Labrador)?

They took wood from Vinland to Greenland. They traded mass amounts of walrus ivory from Greenland to Europe (it was perhaps 99% of their exports), in exchange for tools and finished goods.

The Norse Greenlanders were a European civilization and it was very important to them to keep access to that European trade link. They were not fully self sufficient like Inuit people. So the Vinland settlement was perceived as just a source of materials for Greenland. I believe they likely explored further but any further settlements would have been perceived as too far from the civilizational link in Greenland.