add input and my problem in jQuery

Question

Here are the problems that I'm facing with a small jQuery script :

1. In the input with value hello after I click on add button followed by clicking on remove, The link to add vanishes. What triggers this in jQuery?
2. Upon clicking on add below the second input, a new link for remove is added for each input field that is added, I would want only one remove link that would remove the most recently added input field.

Check out My jsFiddle to see the problems in action.

Answer 1

****** MIND READING MODE ON ******

I think this is what you need:

http://jsfiddle.net/nicolapeluchetti/pgDcq/4/

Tell me if it's ok

UPDATE

****** MIND READING MODE OFF******

Mission accomplished