Applicantmum77, I will try to answer your questions in the order posed.
I can't speak for Interior Design,but the other design disciplines have 90 kids admitted each year.
I don't think that being out of state makes it more difficult since UC wants out of state people due to the higher tuition that they can get.
Being from a small private school which is too small to rank might prove to be a problem. Here is the url for UC's minimum requirements for Interior Designa and architecture:
http://www.daap.uc.edu/said/bsintdes_admissions
What I have seen is that UC is VERY class rank oriented, wanting to take kids in the top 10% of their class. However, if your daughter isn't in the top 10% or isn't ranked, they want a minimum of 3.75 UNWIEGHTED GPA. Frankly, I think it is crazy to not weight honors and AP courses more, but using unweighted GPA seems to be all that they do. I even met a guy with SATs in the high 700s and a great GPA who was rejected because he stupidly applied too late.
I can't tell you what the average GPA and SATs are of accepted students but Interior Design and Architecture are very highly ranked programs in the US, which brings in some top kids.
I would say that if your daughter has a GPA of at least 3.75 and has SATs of at least 1250 ( and preferably higher), she has a good shot.
Remember, UC doesn't require portfolios for admission to most design programs. They believe that a strong academic kid will perform better than one who isn't as strong academically. Thus, their admission policy is one of the more selective academically among the art and design schools.
Also, it is VITAL to apply as early as possible. Many slots are awarded to those who apply early and meet these requirements because UC uses rolling admission. This is also a bit strange for a very selective school,but, again, this is the way they are. AT least your daughter will find out early.
Hope this helps.