fix those geysers, probly by running a new tile line from your pond to above the highest blow out. you should be able to get a 4" tile run for what 1.5$/foot, or so, unless you are in New York City.

to answer your direct questions.
My question is can I route it on to my neighbors land where it use to go? probly, why not, but why

I would like it out of my pond? if I was you, I would want that tile line in my pond, unless of course you can give at least one good reason why you dont want it, but none are coming to me. I would say it is all good, bring it.

How do I determine the natural flow? the natural flow is to slowly percolate down the path of least resistance, probly creating several swampy places that are not possible to maintain for the entire year. perhaps you can dig those spots out and make nice wetlands, if you dont fix the tile?

its better to have too much water and let it out your overflow than to be getting your mower stuck or wishing you had water because your level is lo. the tile will not bring silt. consider it a spring.

dump it in the creek, it is gone.

its all about the water and slowing it up on its way to the ocean.
regards, from Bonny Island