How I can get several Enthusiast badges?
Can I get two badges for visiting the site 60 consecutive days or have I to rest from SO over a day to continue the 30-day cycle?
The Fanatic and Enthusiast badges are only awarded once.
The Yearling badge is awarded yearly (provided you earned 200 rep in that year). Edit- You do not have to visit every day to get this badge...if just one day a year you went to the site and earned 200 rep you could still get this badge.
Easy answer: If you could earn multiple 30-day badges, everybody who has a 100-day badge would have at least 3 30-day-badges. Since nobody has more than one, what do we learn? :)