in the main town. the water city place there should be a nurses office somewhere towards the middle. go there and inside talk to the nurse, she will heal u and your monster for free.
errr and to catch a pet you have to turn off auto battle and then it should be an option next to fight, skill, etc. click catch then click the monster and hit defend. better info would be found here: http://www.monsterandme.com/1about/attach2.htm
Twenty-eight days... six hours... forty-two minutes... twelve seconds. That, is when the world will end.