When I look on line and see the tickets that are up to 50 Euros cheaper with limited availability, if I know where I am going, would it be wise to purchase them right away? Are they offered until a certain date or until they are sold out?
You can buy them from anywhere in the world as long as you've got internet access. Just keep in mind if you have to miss the booked train you'll have to buy a new ticket at full fare then!
Many of the tickets are on sale, but only for a limited number of seats on the trains....once they're gone, they're gone. Bahn.de details what the regular price is, and what the sale prices are, so you can tell which is which. The sooner you buy, the more you'll save.
Is there any problem with buying the tickets from North America on line?
Think of them as similar to Southwest Airlines's different fare categories. The cheaper fares are limited and restricted but sell out first. The more $ you pay, the more flexibility you have. If you know what train you want to travel on now, there is no reason to wait to book.