The easiest way to tell a false morel from a real one is slicing it lengthwise down the middle.  The real ones are always hollow and the false ones are not.

Here is a website the has pictures of false and real morels.

http://thegreatmorel.com/falsemorel.html

Generally, yes that's what I've done.  I was careful to slice everyone down the middle insuring that they were all the real deal before eating them.  I find it hard to believe that having a false morel touch some of your real ones would be enough to poison anyone, but I'm definitely no Paul Stamets so don't quote me.  I've yet to have found a false morel ever so it's never been an issue for me.  Of course I've only just begun hunting morels within the past few years.  Dave, the one who got me into it, has been hunting them for many years so hopefully he'll chime in with some knowledge.

Here's another article I found online:

http://www.thepoisonreview.com/2011/05/29/false-morel-poisoning-in-michigan/

I think proper identification without even picking them can be done relatively easy.  Notice how the false morels have what looks more like a brain fold pattern whereas the real morels have distinct honeycomb like cells.  Simply peruse all the images and I think you will be well prepared and not be fooled out in the field.

I too have yet to find a false morel so i can't really compare on first hand knowledge. I wouldn't suspect the toxins would transfer to the real ones though. Like Scott say, after a good soak/rinse just cut in half, if hollow all the way from top to bottom, you're good to go.

In the field i would suggest a mesh bag (so spores drop out as you walk around) or atleast a brown bag, anything closed or plastic traps in moisture and can rot the morels fairly quickly. Even in the fridge at home, no plastic.

-Dave