For example if US places sanctions on Russia or any other nation then does it has any kind of expiry date after which the sanctions will collapse?
No, there are no practical expiry dates. Even if a sanction did have an expiry date, it could be replaced by a new sanction.
Is there any government organization which reviews whether sanctions should be cancelled or President/Head of the respective states have the sole authority to cancel sanctions?
The main regulator of US sanctions programs is the US Department of the Treasury, Office of Foreign Assets Control (OFAC). OFAC is responsible for promulgating the sanctions regulations, designating individuals and entities to the Specially Designated Nationals and Blocked Persons (SDN) List, and enforcing these measures. OFAC has broad subpoena powers. OFAC imposes civil fines for violations, but criminal penalties are handled by the DOJ. The US Department of State collaborates with OFAC, is also a key player in policy guidance and licensing decisions, and has a primary role in administering extraterritorial (“secondary”) sanctions.
Source: Norton Rose Fulbright
What is the longest sanction against any nation (in years)?
The US sanction of Cuba has been in place since 1962 (56 years).