Answer to 1st Question:
Yes
Explanation:
Since weight is influenced by gravity therefore it is possible for an object to be weightless. A simple example of that is the International Space Station or also known as "ISS", the International Space Station's mass is 440,725 kg (971,632 lbs.) its weight on earth is around 450 tons. On space it weights 0 tons because there's no gravity. Therefore we can conclude that an object with mass can achieve weightlessness when there is no gravity acting on it.
Answer to 2nd Question:
No
Explanation:
It is impossible for an object to exist to have weight without a mass. Why? that is because weight itself is only influenced to gravity therefore massless things that achieve weight are impossible.
