Hypothesis testing based on Likert type data

I know this site is full of similar questions, but either their answers do not apply, or I'm missing something.

I have data from a questionnaire. Responses are in the form of Likert items, some of which can be used to construct a scale. I'm specifically interested in those that cannot be used to construct a scale and should therefore be treated as ordinal.

One of the statements probes an employee's job satisfaction: I enjoy working at the company (answer: Strongly Disagree, Disagree, Neutral, Agree, Strongly Agree).

Another statement probes the employee's organizational fit (for example): I have several friends at the company (answer: Strongly Disagree, Disagree, Neutral, Agree, Strongly Agree). I have defined a hypothesis: Employees with a strong organizational fit will experience greater job satisfaction.

My questions are:

1. In order to reject (or not reject) my hypothesis, can I construct a contingency table and use either Pearson's Chi-square test or Fisher's exact test?

2. If not, can I use this data to test my hypothesis and how should I go about it?

3. If I can, how do I go about constructing the contingency table?: Should I take the response distribution to each statement (e.g. Job Satisfaction: SD = 35, D = 55, N = 40, A = ..., SA =...) and end up with a 5x5 contingency table?

If it matters, I'll be using either R or SPSS to perform the calculations.

(3) The contingency table is the same regardless of what tests you apply to it. It's a $5\times5$ table of counts, as you say. It's not clear why you're asking this, not least because producing it is a simple task in any software.