I didn't try very hard, but I couldn't find a "curl" trademark here for software:
But the law follows "use it or lose it" rules. If you don't defend your trademark, then in the eyes of the court it is no longer a trademark.
Think of the term literally; if it's not exclusive to you, it's not longer a "mark" of your specific "trade". It's just a "mark".
Not true. Unregistered marks can still be defended (it's just harder).
That's why there's both ™ and ® symbols. Trademark and Registered Trademark.