So you only have one outcome variable: whether or not a person graduated from the program. In this case it is probably practical to use a logistic regression.
For the missing data, what are these sets of scaled scores that you are talking about? Do they somehow define an outcome, or are they a set of scores that define your predictor variable? In either case, if you cannot get these scores from anywhere, then whatever analyses you will be running, will be for the 217 people, not 260. There is nothing that you can do about it, but you will have to note it in your report.
As far as the outliers are concerned, I am not sure what you mean that you have outliers for one twelve year old and one 18 year old. As long as the histogram has a normal distribution, you are ok to put it in the model as is. It does not matter that there is only one value for 12 and one value for 18. Perhaps you have to clarify your problem to me with this variable. Also you should make sure that all of your scaled scores are normally distributed. What are the values for the scales? If its a likert score of 1-4 or 1-5, it is considered an ordinal variable, not a continuous variable, although many people use these as a pseudo-continuous one.
For correlations, without knowing more about these clinical variables, I cannot give you anymore advise on how to properly put them into the model. Sometimes a set of scores are combined, if they are all highly correlated, into one score to use in the final model. Other times, they are left as separate scores. Remember, the more variables you put into your model, the lower is your power. As I mentioned before, start by performing simple t-test or a chi-square test for each individual variable in order to decide which one should go into the model. For example, if ethnicity is not significantly different between those who graduated and those who did not, you might decide to exclude it from the full model, or you might decide that it is important enough variable for you to keep it in.
As far as the website which I listed in the posting, it is the website for my private consulting business, where you can go to get more in depth answers as well as some more complicated analyses done for you for a reasonable price. I cannot perform your analysis for you here on talkstats, nor check your data for some other inconsistencies which you might have not noticed. My personal website has nothing to do with talkstats.
Jenny Kotlerman
www.statisticalconsultingnetwork.com