First, Hello to everyone and thanks in advance for any help.

My bathtub used to drain properly (I think.) but not fast IIRC.

I've done some searching around the site and found a few good ideas. So according to some suggestions, I've done the following.

Unscrewed and remove the overflow plate,(The one with the drain lever) and tried ti pull out the tub stopper. But that is where I got stuck. The drain stop would not come out of the top. So I proceeded to pour down some Lime away (green bottle- hard water stain cleaner) and seems to loosen it up a bit when moving it up and down.
But still would not come out to let me use the snake. Bathtub drain itself seem to have not enough room for the snake through!

Impression : Seems when it is draining, it used to gurgle and will drain proper. But it does not gurgle any more. Dose this indicate anything? How to remove the drain stop when it is stuck like that? It does not have any king of leverage for me to force it much.

Anyway, Thanks for your time and looking forward to your help.

PS. I've tried all kinds of cleaners and not helping the drain. All other drains are fine!

Noob ( in plumbing!):p