No. You are not required to be present through any step of the process. However, if you choose to be you are more than welcome to be involved as much as possible.
Yes. It is safe to remove a tree close to the house if a professional is doing the work and is taking safe and professional steps in order to remove the tree.
The professional thing to do is to talk to the neighbor and inform them we might need access to their yard.
There are a couple of purposes when it comes to stump grinding
We would like to get this taken care of for you as soon as possible but we could potentially have to come back to complete this aspect of this job.