I can't answer all of your questions, but I know Kelapo coconut oil, www.kelapo.com, is a fair trade brand and you can read all about their practcies on their website.

Coconut flour may be considered more environmental friendly than coconut oil. I say this because the major commercial products of coconut are copra, coconut oil (derived from copra), and desiccated coconut, while domestic uses are predominantly coconut milk with the residue being discarded. Coconut residue can be milled into flour which can be used in cooking and is a good source of fiber.

I tried to find some better unbiased, science-based links, but this was all I could find. Sorry I couldn't be more helpful. You asked about brands and such, so I found a little bit on that.

                                 ***Human Labor***

1) It seems pretty labor intensive according to how Jamaican Gold gets their raw virgin organic coconut oil through labor intensive methods. You can see their "step-by-step illustration" here

http://www.essentialoil.com/Jamaican%20Gold.html

2) Coconut picking can be a risky job often left for the poor

As he approaches his first tree of the day, S. Mohan presses his calloused palms together and bows his head“Oh God, I am climbing the coconut tree,” he whispers. “Protect me from harm.” With no safety gear beyond a strap of palm frond tied around his ankles, he launches himself onto the tree’s arcing trunk, which rises dozens of feet into the air. With a swift series of spider-like maneuvers, he is at the top of the tree within seconds, slicing the nuts from their stems with a heavy blade he carries tucked into his loincloth.One misstep and he would surely fall, as much as 100 feet to the ground.

http://www.nytimes.com/2009/11/18/world/asia/18india.html?_r=1&scp=1&sq=kerala&st=cse

3) Child labor is used to gather coconuts in the Philippines

http://www.allvoices.com/contributed-news/4137442-child-labor-still-a-problem-in-the-philippines

4) On human labor from Pure & Green Organics brand coconut oil

We choose to source fair trade certified organic ingredients wherever possible as part of our internal social justice policy to ensure there is no child labour used, above average wages paid, and education and health care benefits provided to farmers.

                        ***Sustainability/Environmental Impact*** 

1) Harvesting of coconut oil more earth-friendly than palm oil

As I suspected, coconut oil is a vastly more sustainable product than icky old palm oil, primarily because palm oil production entails razing entire fields and forests of trees—sadly, it is akin to slash-and-burn deforesting tactics used to clear-cut land to graze animals, which is one reason many of us became vegetarian in the first place. This process obviously destroys entire ecosystems, but it seems to have a particularly devastating effect on endangered orangutans. Coconut oil production, on the other hand, entails harvesting the fruits of the tree and letting the tree live so it can continue to produce more coconuts.

http://vegansofcolor.wordpress.com/2009/01/06/japanese-environmentalism-good-news-about-coconut-oil/

2) Earth Friendly Products claims to be sustainable

When coconuts are used, it is considerably easy to replace them. Coconut trees can grow in almost any kind of soil even in sandy soils in seashores. More so, they live and bear fruit for up to more than sixty years. It is considered a "three-generation tree" which can support a farmer, his children and his grandchildren. Coconut oil is regarded as renewable resource which can be grown again in contrast to fossil and mineral raw materials such as crude oil, coals, ores, etc. whose occurrence is limited and finite..Earth Friendly Products uses coconut oil based surfactants as oppose to the palm oil to prevent the environmental and socio-economic impacts of palm oil that have caused substantial and irreversible damage to the natural environment. In addition to that we are aiming to establish a system to promote environmental sustainability in our contracts and purchasing by including environmental sustainability as a criterion for the point evaluation of vendors and contractors doing business with Earth Friendly Products. Earth Friendly Products is working with the stakeholders to evolve the industry to a more sustainable model.

http://www.ecos.com/about.html3)

Kelapo claims to be sustainable and use fair trade when it comes to harvesting for their coconut oil.

The factory also showcases virtually complete recycling of all process by-products and waste: husks are sold for fiber and coco peat, coconut shells generate steam in our boiler and are sold for charcoal and activated carbon, the seed cake is sold for animal feed, and the wastewater is treated and used for irrigation and groundwater recharge.

Even in transport, we employ practices that are supporting the sustainability of our environment. Our shipments are packaged in special totes that can store as much as two to six steel drums in 20% less space. Plus, the totes contain no metal and are completely recyclable and biodegradable.

Additionally, the “Fair for Life” premium we pay on all coconut oil purchased from Sri Lanka, supports a wide range of community development projects, including worker’s welfare, education, and health care

http://www.kelapo.com/fair-trade-coconut-oil/#fairtrade

The environmental impact of palm oil (since you mentioned it) is due to deforestation and tendency to grow it monoculture. This also happens primarily in SE Asia. Palm oil from Africa is considered sustainable (and delicious!)

See: http://en.wikipedia.org/wiki/Environmental_impact_of_palm_oil

For coconut oil, I don't know.