Ownership does not require a physical presence by the owner. There are challenges to remotely managing any company at any stage, ones I would suggest you avoid if there is any possibility to be present. This applies to mature global companies with many offices as much as it does to startups.
There are advantages of being in someone's presence that tele-presence will never replace. You can't be exposed to human subtleties of proximity when you have no proximity. And while you may be able to get work done, it lacks some of the character that comes from being in someone else's space. There are numerous valuable cues that are missed and opportunities to connect missed, when you have no chance of being in the same space.
Like I said, it's possible to operate a company that way, but it won't be as good as if you work with a team that is in your physical space. There are distinct benefits to accessing remote resources that could be in limited supply in your proximity. You will want to think about what such a convenience costs you in overhead and lack of interpersonal connections that can only happen in a common workspace. Is it enough to justify the exchange of value?
It is. US laws are very favorable for business and with the right corporate and management structure, you can do it pretty easily.
Why are you asking? Is this proximity to the market you are pursuing, a pseudo-geo credibility, or some other reason?
Sure. It's best done with a C corp you can create by going to legalzoom.com
You will need to hire someone local to help you with taxes. You need to be careful about how you manage relationships between your US company and your original company.
You can actually use a non-US company to do this but it is really really inadvisable to do so. You want to containerize all your US business inside a US company.
Yes, but you need to visit atleast once for opening bank accounts etc