Rotating a staircase and making a new landing. How do I support it
You've asked some good questions.  However, your project is going to be a bit easier than you think!  You won't need a column &amp; footing just to erect a small landing to re-route your staircase.  If you have any doubts, you can consult an engineer, who will accept your money and then tell you the additional dead load from the landing is no big deal.
So how do you support your new landing?
You can frame it directly on top of your plywood sub-floor.  You'll be building a short L-shaped wall to enclose the new landing.  This is accomplished with ordinary 16&quot; on-center 2x4 framing.  Support your relocated 5-step staircase the same way.
Blocking between the I-joists
You should install blocking between your I-joists to provide additional support for the wall(s) which will support the landing.  Do that before erecting the walls, that way, you can nail the bottom plate of your new walls, through the subfloor, and into the blocking.
More resources
My guess is you may not have much experience with framing.  Check your local library for a book about framing walls.  I like the Black &amp; Decker Complete Guide to Walls &amp; Ceilings and it should be easy to find in many libraries and home improvement stores.  Also, the book Building Stairs by Andy Engel is really great, with lots of illustrations, and I think it will help you a lot with your project.  In particular, it may give you some extra confidence when building your new handrail posts.
I hope this helps.