By choosing appropriate numbers to write at the start, you can manage it with
eight questions.
Here's how.
Choice of numbers
The numbers you should write at the beginning are
the powers of 2: $1,2,4,8,16,32,...$
Let's label the numbers, in the new order as they're laid out face down, $a,b,c,d,e,f,g,h,i,j,k,l,m,n,o$.
Every time you ask a question about some subset of consecutive papers, you know
the exact (unordered) set of numbers on those papers. This is the maximum amount of information you can get from one question, since knowing the sum cannot tell you anything about the order.
Note that this condition (in the last spoilertag just above) is the important thing. There's nothing special about the particular set of numbers I mentioned: you could as easily use
e.g. powers of 10, which would make the required deductions quicker for those not used to binary representations.
Choice of questions
With your first question, you choose
$a,b$.
With your second question, you choose
$b,c,d$. Now you know exactly what $a$ and $b$ are, and you know the unordered set $\{c,d\}$.
With your third question, you choose
$d,e,f$. Now you know exactly what $c$ and $d$ are, and you know the unordered set $\{e,f\}$.
Keep going in this way, choosing
$f,g,h$ then $h,i,j$ then $j,k,l$ then $l,m,n$.
After that, you know
all numbers except $m$ and $n$, which you only know as an unordered pair. One more question is enough to know which is which among them.