I have an porch which is supported with laley columns. It is not very
old and it is in excellent shape. I want to make it into a heated
room. Is there a way to put a standard poured foundation under it and
somehow connect the botom of the sills to the wall? The columns are
solid, there are no saging or springy floors. I just feel that a
foundation is better.

Sure... this is an easy one.

Tear out the porch and pour a foundation. Then, build the walls and add
the heating.