if there is a lot of co2 in atmosphere why not "mine" it?

There is no financial incentive to mine it, or to do anything about it. Your suggestion is indeed something that in the long run probably has value but right now there is no money to be made at it. Last year the U.S. House of Representatives tried to make a law that would make it profitable for companies to invest in that type of technology but the Senate refused to act on it. Now, the new members of the House are also saying that they refuse to make battling CO2 profitable until floods as devastating as the ones in Pakistan and Australia are happening in their own state. Our Congress has taken the position is that we will do nothing until people start dying. Unfortunately they will all be dead before the see the obvious results of their decisions.

Yes plants do use CO2, but you need a lot of plants and remember you then need to preserve that plant material to keep that C locked away. If you let the pant die and decay...well all the captured CO2 is returned to the atmosphere.

CO2 has almost no economical value. CO2 is available in almost pure form from several industrial processes so why would anyone go to the expense of extracting it from the air? Actually they do when they liquefy air, but most of it is hen used in processes that return it to the air.

Because a plant in a classroom cannot really be compared to the entire planet? The planet is trillions of times larger than your classroom.

Increasing forest cover would certainly slow the growth of atmospheric CO2 concentrations. Unfortunately forest cover is *decreasing*, not increasing, and deforestation itself accounts for about 25% of global CO2 emissions.

There are a lot of ideas to do this; for example see these : http://www.americanenergyindependence.com/recyclec... - I can't vouch for the site's accuracy but these ideas have been bandied about.

I have no idea how feasible any of this actually is. As pointed out, it takes energy to extract CO2...