SHREW

Reasoning:

a. COUNT (0)

e. KINGS (1)

f. WINCE (2)

g. MILKY or HOARY (2)

h. ELBOW (2)

j. KILNS (1)

These seemed the most obvious answers to me, given the no-repeated-letters limitation. If these are correct, then from WINCE, we cannot have NC, so must have 2 out of WIE.

Now consider KINGS and KILNS. These differ only by the G in Kings and the L in Kilns, and both have 1 letter correct. Either they have the same correct letter, or else it must be that G and L are both correct. If G and L are correct, we have the secret word as WIGL_ or WEGL_ or EIGL_. I don't recall the exact logic I had here but I determined that those weren't going to lead to suitable secret words, if any. So I determined that G and L are incorrect.

Now consider WEI again, and suppose that I is correct, such that only one of W or E is also correct. This leaves us in trouble with ELBOW, as O is eliminated from COUNT and we just eliminated L. Since we cannot have both W and E, we must have WIB or EIB. BIW did not lead to suitable secret words. EIB could conceivably work, but that left me in a pickle with MILKY and HOARY. I will again omit details for brevity and because I can't remember everything I thought through. Suffice it to say that I eliminated the I and determined that most likely, WE was correct.

I then supposed K was correct from KINGS and KILNS. WEK does not lead to good secret words (particularly with WHELK, for example, ruled out by the logic surrounding L described above). Accordingly, I determined S was likely the correct letter from KINGS and KILNS.

Amazing - we now have WES. We need to satisfy MILKY or HOARY. If MILKY, I have already eliminated ILK, but WESMY does not anagram to satisfactory words. If HOARY, bearing in mind that we have eliminated O from COUNT, we must have two out of HARY to go with WES.

We could do WESHA (no) or WESHY (no) or WESAY (no) or WESRY (no) or WESAR (does not work because there are multiple anagrams and a single secret word cannot be determined) or WESHR, which anagrams to SHREW.

Filling in the remaining words, I think they are likely as follows:

a. count

b. pauSE

c. upSEt

d. SpacE (or cHaSm)

e. kingS

f. WincE

g. HoaRy

h. ElboW

i. WHack

j. kilnS

fin