Was this the first interview or just a talk?
There is no such thing as "just a talk". Unless the person hiring you is a family member, because then the person might have reason to talk to you about something other than work. Even then, though, you can consider the entire time period as being a sort of interview.
For that matter, your entire life may be up for inspection, and considered to be fair game for an interview. (Well, okay, I withdraw that stance slightly, since there are government-protected details that officially should not be considered as part of the hiring process. But, unofficially, they often may be.) These days, many company check Facebook accounts to see whether you seem like a focused person who accomplishes things, or brag about getting drunk and high frequently and badmouthing current or former employers.
Or there is no consensus about it?
P. Hopkinson's answer and first couple of comments are right; every interaction should be considered part of the broad "interview process". You see multiple answers saying the same thing, with no highly rated answers saying something different. So, yes, there is consensus on this.
Are such Skype or phone dialogues under the category of "first interview"?
Sure. I recall one of the best jobs of my life started out with a phone interview. Then, he asked me to come in person, so I could meet the team.
And at the end he said he will invite me to the company show around and talk to other colleagues.
That's a great sign. The hiring manager likely values the time of your other colleagues who are already hired. Your hiring manager wouldn't want to bother your potential future colleagues with meeting you unless you were a pretty serious candidate.
Just beware that there are predatory people and even organizations that pretend to offer you a promising rich future, only to say they need things from you like your social security number. (This is a particularly devastating reality, since legitimate organizations also ask for this same information.) A blind interview when using video technology seems to me like a pink flag-- not quite red, but some concern. With scammers being so elaborate that some Nigerians even created a fake embassy which seemed official to basic scrutiny, perhaps all you can do is try some basic research to see if the organization seems legitimate. Such research may also be helpful for an ongoing interview; I recall once an organization's president was happy that I knew at least a tiny amount of basic information, which showed that I invested at least some effort in trying to learn about the organization.
So, I can't say that all of this is definitely a good offer. (Even some legitimate employers, who will actually pay you, may represent offers of bad employment situations.) What I can say is that what I'm reading sounds pretty promising and overall pretty consistent with a good situation. It does sound like you passed the first hurdle. Congratulations. Stay persistent in your efforts. Good luck!