1) So basically for each tab subscribe on a click.
On tab click event handler you can reach to sender property which is actually the tab object.
Within this tab navigate (find) drop down list with usage of:
var dropDowm = $("#nameOfYourDropDown");
Then you might need to get some data from Web-service by requesting it with help of either $.Ajax or $.getJson methods.
In core of web-service i can advise to you to use either REST WCF or ASP.NET WebApi, by reason, that they use lighweight messaging pattern.