does the weight of a plane changes if the birds inside it are flying, and if not?

Answer 1

It depends on whether you are talking about:
dead-weight or
w=mg.

And whether or not the plane is sealed.

IF THE PLANE IS SEALED:
If you are talking about dead-weight then the weight increases when the birds perch because the birds are supported by the structure. When the birds are flying, although they are contained within the plane itself their weight does not contribute to the downward vector force of the plane's structure due to gravity.

If you are talking about
w=mg
then the weight remains the same. Since the birds are inside the plane and the plane is sealed, they may be considered to be a part of the internal mass of the plane.

IF THE PLANE IS NOT A SEALED CONTAINER
If the plane is sitting on the ground with the hatches open, than the birds can not in any way shape or form be considered to be part of the plane's mass. In this case you are talking about the weight of the plane PLUS the weight of the birds.
.

Answer 2

If the birds are flying, they don't add to the weight of the plane. If they are sitting they do. This is because if they're flying they are not in contact with the plane actually, so there can be no transfer of weight or force.

Answer 3

No. The weight of the birds is supported by the air around them, which in turn is supported by the floor of the plane. So whether they're sitting or flying, the plane still supports their weight.