Yes it can own land. Costa Rican law allows one to utilize a corporation, LLC or trust to own land even when this entity does not conduct actual business in the country.
Yes, foreigners have the same rights to own property in Costa Rica as its citizens. This includes ownership of property by a US-based trust or a trust with a US citizen as its grantor or trustee(s). The only exception is concession property or land ...
Patenting property in one's own name and then exchanging the property into the trust will merely transfer deed with clear chain of title. And in some countries like Australia where a stamp tax is charged for each transfer, that extra step could be ...