Is there a way to get a box to appear beside the current one to show function params and description? Examples of this include Eclipse, visual studio and flash develop.
Really this is a scintilla question - I know that you can get call tips to show the function parameters of a function, but I don't think it works in conjunction with Autocomplete. However, using a User List you might be able to emulate it perfectly (you get an event as to which entry from your list is selected, so you can "autocomplete" without filling the complete function signature out. Have a look at http://www.scintilla.org/ScintillaDoc.html#UserLists, which maps to editor.userListShow(int, str), where the int is the list type (probably not important for you), and the str is the joined up list of entries.
Please note that in 0.7 removing an event handler (ie. calling one of the editor.clearCallbacks() functions) whilst in an event can cause a crash. The test version on github.com/davegb3/PythonScript under downloads solves this problem.