Sometimes yes, but not always. Whether local or international, you SEO efforts will determine your overall success.
local host company be better?
Nope. At least not in the 21st century. There has been many developments in this area. It doesn't really matter nowadays where you host your site.
It is not that obvious. I also depends on your niche and your local SEO efforts. Gone are the days when domain names mattered. Now it is just SEO.
Not any more. That used to work back then, when the search engine bots were not as smart as they are now.
The world is now a global village. Whether your site is hosted by a local or international host, it doesn't really matter. How you do your SEO matters most.