can anyone explain how Fanatic and Enthusiast badges' criteria works?

Enthusiast and Fanatic badges are awarded for visiting the site on consecutive 30 and 100 days respectively. As mentioned here, what counted as a visit is not public, but from what I've observed, you have to visit home page or your profile page.

Enthusiast needs 30 days. so do I have to come here every 30 days for 30 times?

Yes, you have to visit any page of the site including home page, any post etc for mentioned days to get this badge. But not for 30 times, just 30 days.

And yes you have visited the site for more than 3 days, but you miss one or two days every time. Remember, missing one single day will reset the counter. You don't have to login again, because it won't matter. What matters is your visit on the site.

can anyone explain how Fanatic and Enthusiast badges' criteria works?

Enthusiast and Fanatic badges are awarded for visiting the site on consecutive 30 and 100 days respectively. As mentioned here, what counted as a visit is not public, but from what I've observed, you have to visit home page or your profile page or any post.

Enthusiast needs 30 days. so do I have to come here every 30 days for 30 times?

Yes, you have to visit any page of the site including home page, any post etc for mentioned days to get this badge. But not for 30 times, just 30 days.

And yes you have visited the site for more than 3 days, but you miss one or two days every time. Remember, missing one single day will reset the counter. You don't have to login again, because it won't matter. What matters is your visit on the site.