Weight Painting and Rigging Problem

Hi, I was your student before in Blender Course and I have a problem with my character modelling.

I made the armature and got some problem about weight painting. The vertex that should not be included, was pulled to, when I was trying the spine bone. Here are some pictures, hope you can help me.

And here is one with the neck bone.

If, I use auto rig/ rigify there would be holes in my model. What should i do to fix this?

Thank you in advance =)