Is your hosting firm important for your ranking in google ? Is your url extension important for your ranking in google ?
Your hosting provider doesn't play a role in search engine rankings, just make sure to use a hosting company in your country. Domain extensions do not give any special weight to search engines either, basicly a *.com can rank just the same as *.edu, there is no difference.
I agree with ssandecki. Make sure to use domain name related to site and hosted in country you are promoting to.
I've heard that getting links from .edu and .gov are a lot stronger than .com .net etc... The reason behind is that those links are generally from established and respected organizations so the links are more relevant.
.edu & .gov have no special extra weight, many .com and .net and .org rank much better than .edu or .gov
It depends on how you optimized the keywords on your page and the quality of links connected to the URL.
is it true that Google give more weight to .com compare to .info domain ? I was told that Google tend to give .info less priority nowadays. This is because .info being used by a lot of spammers as it's the cheapest among all. not sure how true it is but I noticed most top 10 websites are .com domain.
To add to that, of course country specific domain names has an effect while ranking in those country specific search engines