First off - the cat has been to the vet and they have run some tests.
However, the test results will not be back for 2 weeks (?).  But if anyone
has any thought on what might be wrong it would be appreciated so she can
either breathe easier or prepare for vet bills.

She got the cat 6 months ago and the cat was supposed to be between 1-2 years
old.  The vet has told her she is more likely between 5-10 years old.  She is
now an inside cat but was an outside cat.  She has been declawed (before my
friend got her).  She first noticed some hairless patches on the cat a couple
of weeks ago.  They are increasing in number and getting larger.  They are on
the neck and head area and don't seem to be in spots where the cat could be
chewing on them or otherwise causing the problem.  The cat is also throwing
up but no hairballs or anything.  She also has loose stools.  At first I
thought it might be ringworm but it seems like the vet could diagnose that by
seeing it without running extra tests.  The tests are for other kinds of
parasites.

Any thoughts?