>>Second, what are the chances of saving it?

I'd say, pretty good.  If the tree had a fairly soft landing, the queen may be alive.  Some combs could have lost their anchorage, some bees may have been crushed, and some honey may have spilled.  The bees have started any repairs as soon as the tree was down.

>>How much work is involved?  Something a hobbyist could / should tackle?

Yes to 'could' and up to the person if 'should.'  A hobbyist can get great satisfaction from this sort of accomplishment.  I would do it for a fee.  I'd puff some smoke into the nest.  I'd use a chain saw or a reciprocating saw (sawzall) to open up the nest starting at the entrance call.  I'd use a bee vac to right away collect any alarmed bees at the entrance.  The noise and vibration of the saw will make some bees defensive but not nearly to the extent you'd expect.

I'd then proceed to vacuum up the bees as I'd carefully cut out the combs and placed them in box lined with plastic.  This could take a while.

You can tie the combs in wooden frames for the bees to use.  I don't unless I am absolutely sure the colony had not been sprayed with insecticide.  I place the brood combs over a queen excluder on top of developing nucs.  When the brood has emerged, I remove the combs, and melt them down. 
   
The collected bees can be dropped into a new hive.  After a couple of days you should be able to tell whether or not you got the queen.

>>Third, if it comes down to exterminating the hive, what is the best 
recommended procedure?

I have never exterminated a hive.  Soap water has been mentioned. 

Waldemar

PS.  If you don't have a bee vac.  You can still cut out the combs with the bees on them.  I don't but you might wear gloves.  I use my bare fingers to gently push the bees out of the way to grab hold of comb.  You'd be surprised how bees will move out of the way for you but, if a bee is down a cell I will occasionally get stung.

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