How to fruitfully utilize faculty-student orientation sessions at institutes you don't want to attend?
I don't think you can expect to get the opinion of a professor about another institute/lab. You can probably get some facts (like this other institute has more/less money, they are more/less active in this area), but nothing subjective. Academia is pretty small world, and people try as much as possible not to say anything negative publicly (and since everything said is positive, it can be hard to distinguish the real positive from the fake one). 
You need to have a real interest in their work. As mentioned here, it's already pretty hard to maintain collaboration between people interested, so if there is no clear interest, it will very hard to be on email terms. But, the question is: why do you want to be on email terms? 
See the previous point. You need to really interested, meaning you've read and understood their papers, and are able to ask questions that go beyond "what are the possible usage of your approach?". 


As a general remark, professors are usually already very busy dealing with their own research/teaching/students. Of course, they usually are open to new collaborations, but they might lack the time to work with a student who is not theirs. A good solution could to try to visit them, academically speaking, for a month or so, to work on a very specific topic.