Yes, you may modify many templates within the JFH service. This includes the forum rows, board statistics, profiles, and more. Please see the HTML Templates guide.
The easiest place to acquire a new skin would be the Skin importer option located in your ACP (ACP → Skin & Templates → Import Skins ). The importer has a selection of many fine skins that you can import with one click. (It also has the option to preview a skin before installing it so you can see whether or not you like it before committing to installing it.)
(These skins are bundled in .xml format for easy loading. To load them in please read this article from the wiki on how to import .xml files.)
There are many other 3rd party resources for Jcink Forum Hosting skins as well.
= Jcink Forum Hosting does not take skin requests nor do we offer a skin request service. There are 3rd parties who advertise such services, however Jcink.com does not make any guarantees, promises, warrantees or claims to the effectiveness, availability, cost or quality of any of these services. They are undertaken at a user's own risk.
Yes. Feel free to modify the skin as you desire/see fit. However, leave the credits for that skin intact. Several skins are known to experience issues if you try removing the credits from them.
JFH offers a fairly extensive list of resources on how to create skins and customize skins yourself, these resources are available here.