2. Can Gliders take off and land at any airport/airfield...or are there known designated airports?

Legally, we can take off or land at "any" airport, but naturally, there are practical exceptions. You wouldn't want to be in the traffic pattern at say, Dulles, O'Hare, Atlanta-Hartsfield, etc.

Most glider operations are located at untowered airports, surrounded by "uncontrolled" airspace. Of course, there are lots of exceptions, but suffice it to say that you probably will be flying with an operation that has this issue resolved and you don't have to worry too much about excessive commercial traffic.