Hi Rajeev, and welcome to the lithosphere. To answer your questions:
1) Yes you can get the the latest topics for a category. Try /restapi/vc/categories/id/support/topics/recent
2) Yes you can customize the date format to an extent. The Date Format is a text property which by default displays MM-DD-YYYY. You can change it to display something like DD-MM-YYYY ex: http://supportcommunity.swisscom.ch/t5/Welcome-to-the-english-help/bd-p/welcome_en or utilize the friendly dates option in the community admin.
3) Unfortunetly Lithium doesn't have javascript support for that at this time. However, you could write a custom component and add your own javascript code to acheieve the effect you are looking for.