It is impossible to perform factor analysis on a single variable. Begin by reading the excerpt of the tag wiki for factor-analysis (hover your cursor over this tag). The smaller number of factors in your single variable case is zero. You have no covariances to consider except the item's own variance. It simply doesn't make sense to try factor analysis on one variable.
Your next step should probably be consulting with your advisor. It sounds like he or she has tossed you into the deep end without a life preserver. Fortunately, there's plenty of information already here, and on Wikipedia, and in books, that could've told you what I've told you in the above paragraph. What your advisor actually wants to know is what none of us can tell you. Chances seem good that your advisor had nothing unusual in mind. Hence I again suggest you read Wikipedia, search for an introduction to factor analysis, or read a statistics textbook chapter on it. Any of these will answer the simple question of how to perform a factor analysis. How to do this in SPSS specifically would probably be judged an off-topic question.
Edit: Thanks for adding the path diagram. It looks like you have five constructs in a structural equation model. With only one variable for Behavioral Intention, you probably won't want to include it in a factor analysis unless the objective is to demonstrate that it doesn't load as strongly on a factor as the factor's intended indicators. Factor loadings are correlations between a latent variable and manifest (measured) variables. Ideally, each item that measures a factor will have a loading above $\lambda\ge.7$, meaning the factor explains at least 50% of the item's variance. For instance, you'd want the items that measure Innovativeness to have factor loadings $\ge.5$ (being a little more lenient and realistic) on a single factor, and items that measure other latent constructs (including Behavioral Intention) to load primarily on other factors, or in the case of Behavioral Intention, weakly on all factors (say $\lambda\le.3$ or so).
If you were to factor analyze all your items, you'd hope for a four-factor solution (i.e., large eigenvalues for the first four factors that descend gradually in magnitude, and much lower, roughly equal eigenvalues for all others after the fourth). Parallel analysis or VSS might be the easiest analyses to interpret if you're inexperienced with reading scree plots or choosing the number of factors by other means. Your path diagram indicates expected relationships among these factors, so use an oblique rotation, not an orthogonal one, after extracting factors (again, hopefully four will be the right number). This will give you factor pattern loadings that are worth interpreting as described above: all items intended to measure the same factor should load strongly together on the same factor, and have weak loadings on other factors. Your one item for Behavioral Intention should load weakly on all factors.
If you were to just factor analyze the items for one factor at a time, you'd want to see a single-factor solution for each, and all loadings on the general (first) factor greater than $\lambda\ge.5$ or so. You don't need to rotate a single-factor solution. If you were to add the item for Behavioral Intention to the factor analysis of any single factor, you'd just want to see it have a much lower loading, lower communality, or higher uniqueness, as compared to all the other items. This should be an easy-enough way to test its discriminant validity; e.g., factor analyze all the items measuring Innovativeness together with the Behavioral Intention item. However, one problem with this method is that it would increase your Type I / false alarm / $\alpha$ error rate to perform the comparison multiple times. Might be worth doing anyway though just to be overly liberal in your discriminant validity problem detection approach.
Since it looks like you have preexisting theoretical measurement models available, you could also (probably should, really) use confirmatory methods like structural equation modeling (SEM). Modification indices could tell you if an item from one factor correlates too strongly with a factor it's not supposed to measure directly. However, I think Amos is the SPSS brand SEM software, so you might need access to that to perform this analysis without learning a new software environment. (Like R! I could even give you code in that, but not in Amos...)
Best Answer
My answer is based on making some assumptions about your question.
Assumption 1: Dependent variable is binary.
Assumption 2: Independent variable (predictor) is ordinal.
Question 1:
If these assumptions are accurate, then the answer is yes. A binary logistic regression would be appropriate as the type of regression one runs is dependent on the dependent variable. A helpful hint is that if possible, have your independent variables have a meaningful 0 (e.g., "never" or "neutral" or sample mean). This tends to help with interpretation of the regression weights.
Question 2:
Based on the information you provided, it sounds as if you have the individual items of a scale (or subscale). For example, if I have 3 questions about different symptoms of a disease, they should factor together. I could average these items or sum the items to create a scale score that is then used as an independent or dependent variable in regression. This is commonly done in many different fields (particularly any field that uses surveys).
Hope this is helpful.