What peculiar ministries or political organizations does Iceland have beyond the Ministry of Fishing and that comittee that approves neologisms in the Icelandic language ? On a similar note, does Iceland have a separate Ministry of Agriculture or is it just lumped in with some other related ministry?
How big is Iceland's trawler fleet ? Do you need to be a member of a bigger fishing company to be a part of the fishing business or can you work in it as a regular self-employed tradesman ? Are sail boats still used on Iceland for anything other than recreation (i.e. passenger or small cargo transport) ?
Where are the largest "woodlands" in the country, outside of city/town parks ? Does Iceland have any known extinct species of plant or animal ?
Amusing questions. I will have to admit my ignorance on a few things.
The ministries are in a flux at the moment. Before the crisis there used to be 12 ministries but they have now been merged to save money, example:
The ministry of fishing has been merged with ministry of labour and industry, as well as the agricultural ministry to create one ministry of labour. The commerce ministry has gone under the ministry of finance. The ministry of social welfare has merged with the ministry of health to create the welfare ministry and the ministry of communication/transport has merged into the ministry of churches/justice to create the ministry of the interior.
This might be reversed by the next government (likely conservatives but really who knows...

I say it´s unpredictable at this moment what the political landscape will be). So the peculiar ministries created to give chrony politicians a boost in salaries have gone.
But the naming commitee is still around. (And is one good reason to condemn bipartisanship, if both sides agree then it´s a horrible idea). They can in theory ban names that are in bad taste but usually just ban stuff that doesn´t fit into Icelandic grammatical traditions.
Example: My cousin has newly given birth to a son. Her husband is English/German and they wanted to name him Noah. (I think his grandfather on the english side is also named Noah and well, there´s nothing wrong with the name).
The naming commitee said they should use the icelandic version: Nói. But they insisted understandably that they still wanted to use this foreign name. Well, the naming committee then said: We can´t have it. And that was that.
No but seriously

or well

, I don´t know which smiley represents my feelings.

Perhaps this one as an embarrasment of sharing nationality with these clowns.
Number of trawls: No idea, (google told me about 60 something...). You can make a living out of sailing on your own for fishing if you are lucky enough to have quota. I know about a few cases, not common but existing. Generally quite well off too.
Edit: yeah, the great Auk went extinct in the 19th century. Apart from that no. There are forests in the north but not really in the same sense as in other countries. The forested areas are neither natural nor large. We have natural birch tree growth, I suppose you could call some areas quaziforested. That being said Hallormstaðaskógur can be pretty, as well as Vaglaskógur.
(Link to a song about a springnight in Vaglaskóg)