1) Smacking != dumping.You could smack it with a neutron star so hard that it would blow it to smithereens, which would lack the mass to sustain fusion.Not only that, but there's literally nothing you could dump on the sun to put out the fire.Yeah, the flame retardant to put out the sun would be pricey. Water would just evaporate in the vacuum of space. But maybe the question is "Why hasn't that prick Newsom developed a way to put out the sun?!"citation please. Thanks.For 10% of of the cost of the fire, they could have had a fire department that could put out the sun.I’m sure that if the government would try to invest the money it would take to prepare for such a fire they would be voted out for wasteful spending
2) I can't picture any way this could happen. The neutron star will punch a column through the sun but it won't impart any great outward force in doing so.
However, in another way you are right. If the neutron star is close enough to the critical mass it might go down the rabbit hole and suck the sun in with it. If you want to blow it to smithereens you'll need a white dwarf very close to the limit, suck up enough that it goes supernova.