How does a nebula form from a neutron star

Here is my understanding, please correct me if I am wrong, thanks

At the end of the giant stage of a star, it experiences a supernova explosion, and turns into a neutron star (could be pulsar) or black hole, the explosion releases a lot of its matter.



Here is what I don't understand:



1 there could be nebula around a pulsar, where does the nebula come from, is it simply the matter released in the supernova explosion? Or it keep releasing from the pulsar?



2 for smaller mass stars, at the end of red giant stage of a star, a planetary nebula forms before it turns into a whit dwarf, is the planetary nebula the same thing as the nebula of a pulsar? only the planetary nebula formed in a less violent way, while the pulsar nebula is formed from supernova explosion?



3 why it is said that the pulsar nebula needs to be powered, by the rotational energy of the pulsar? is this amount of energy used to against the gravitational force of the nebula, to prevent it from collapsing?



Thanks