No answers, but some questions. Note that *nix operating systems are network oriented by default. The computer might, for example, be contacting internet time servers to ensure that the computer clock is accurately set.
What are some of these external ip addressed to which you refer? Have you tried doing a
whois on some of them? That might answer many of your questions as to whether they are mailicious. See
man whois for more.
Have you closed all but essential outgoing ports in your router? For most home users, port 80 for the internet and email ports are the only essential outgoing ports.
Email ports can vary depending on whether you are using POP or IMAP, with or without SSL or TLS.
My gut reaction is that you are have nothing to fear, but, the more specific information you provide, the better we can help you. One thing I can assure you of is this: if you want to improve security, running Windows is not a strategy for accomplishing that.
And don't apologize for your English. It's better than that of persons I deal with every day here in the States.