They should put their money where their mouth is and spend at least a few decades in such countries before criticising others who've made a choice to leave(for various reasons).
Do you know how many children are living on the streets in Havana? Or how many die of starvation or exposure? Maybe they're poor, but they are alive, healthy, fed, and have a roof over their heads. That's a lot more than Americans can say about the at risk in their own country.
I am by no means suggesting that Cuba is a utopia -- my own standard of living is probably quite a lot higher than the average Cuban's. I'm lucky in that way. That's not the case for many, many others.
Presumably all states do.
>Who manages the trade between the countries?
Communism is about owning the means of production so presumably the people will act through their government to decide on trade.
>Are the members of a society that claims to be Communist actually so if that society at large is part of a free-market?
Presumably, unless you mean to say that no actually Communist state has ever existed! (I'll accept this of course, I'd just like you to say it.) If you'd like to know more about this conflict I'd pull up the wiki article for "socialism in one country."
>This sounds like not getting rid of exploitation, but rather sweeping it under the rug and outsourcing it to a free-market entity.
Well the end-goal would be world communism without government, democratic everything, "from those... to those..." kind of world. In the interim trade would be necessary and you're right that unfortunately that trade may come from exploitation of the working class in another country. But if we can take our country, go socialist, reduce exploitation then that's still an admirable goal. Hopefully, those elsewhere will see and follow. I wouldn't call it "outsourcing exploitation" because presumably the trade level wouldn't increase dramatically after becoming communist. It's more like fixing our exploitation while admitting we may not be able to end all exploitation.
NOTE: I'm not actually a communist and I only know a little so these are the best answers I can give. A real communist would probably school me on this.