Free trial premium membership

Sort of. You have to provide a credit card to get a free trial. If you don't cancel, they charge you.

https://support.chess.com/customer/en/portal/articles/1444921-why-must-i-enter-credit-card-info-to-start-a-free-trial-

Is it worth trying?

It took me a little over a year to jump into the Premium Membership pond.  

Just as it appears that you are doing, i was using the site a lot, taking advantage of the free tactics, lessons, forums, etc.

Eventually, i started to feel guilty, realizing that this is a pretty excellent setup to be getting for free -- if it weren't for paying members, none of this would be possible.  Or, maybe it would be possible, but it would probably be a lot crappier.  And, hopefully, as more people buy in, the site will get even better, and at a more rapid pace than it would otherwise.

"Is it worth it," in the 'selfish' sense?  Well, not having to deal with the ads is really nice, but maybe i'm more irritable about that sort of thing than most.  And you get at least 25 tactics/day instead of 5 -- i really dig that.  And creating tournaments is fun.  Etc., etc.

I don't know much about the Indian monetary system/situation, but the Gold Membership comes out to less than a dime per day in U.S. money -- i figure that that's the very least i should be contributing.

Please check your inbox.

I'm sure the staff can answer this more eloquently than i can, but they would basically tell you that they don't charge the card until after the free week has ended.  If you decide you don't want to purchase the membership, you simply let them know before the week is up, and that's it -- no charge to your credit card and a genuinely free week.

And notmtwain already mentioned this in comment #2 -- did you accidentally skip over that part? 

can I do a free trial for all three memberships or just one?

https://support.chess.com/customer/portal/articles/1444776