It looks like there might be multiple issues here.

The query to change Jan. 2 15 AD to the gregorian calendar seems to work fine when I try it:

http://www.wolframalpha.com/input/?i=convert+julian+date+Jan.+2%2C+15+AD+to+the+Gregorian+calendar

I don't see some of the other problems you mention. Can you link to them?

As you noted, the BC years appear to not work. When you see a query not working, you can always leave a feedback for the Wolfram|Alpha team by filling the form at the bottom of the website. I've done already in case you don't see this.

CalendarConvert and DateObject are expressions in the Wolfram Language.

CalendarConvert[DateObject[{-10, 1, 8}, CalendarType -> "Julian"], "Gregorian"]

WolframAlpha tries to support natural language. To evaluate Wolfram Language expressions, you would use Mathematica or Mathematica online.