I do not have to take a language as a requirement, but I want to take Spanish to not lose what I know. I was wondering if it is okay for me to take Spanish 107. 

You need to take the placement and enroll in the level corresponding to your score, even if you do not have to take a language as a requirement. The only 100-level courses in which you can place are SPA 101, SPA 103, SPA 105, and SPA 108. In order to take SPA 107, you must have successfully completed SPA 102 or SPA 103.  

I am a Sophomore/Junior/Senior student. I took the Spanish placement test at the beginning of my freshman year. Can I still enroll in the course corresponding to my placement back then?
No. Since language knowledge is a set of skills that depend on day-to-day practice, placement scores are only valid for one academic year. You will have to take again the placement test and enroll in the course corresponding to your current score.
I got a 5 on the AP Spanish language test and I'd love to continue to take Spanish at Princeton. Should I take the online placement test in order to be placed at the appropriate level that is 200 or above?
Students from the Class of 2026 who receive a 5 on the AP Spanish language test (and commensurate scores on the IB, A-level, or SAT II as described in the AP table) do not need to take the Spanish placement test. Regardless of the year you took the test this satisfies the language requirement and places you into 200-level SPA courses. However, you do need to have your official score report sent to Princeton. Students from the Class of 2024 and the Class of 2025 may have to take the Spanish placement test to confirm advanced placement.
Will I need to have an interview with a teacher as part of the placement test?

You will need an interview and a confirmation test ONLY if your score is higher than SPA 108. The oral interview will be successful if your listening comprehension and speaking skills are both similar to those of students who finish SPA 108 with a B+ (ACTFL Intermediate High proficiency level; see description below). Students who took the AP test or the SAT ST test and obtain a score of “interview” in the Spanish Placement Test will not need to take the confirmation test.
Listening : Able to sustain understanding over longer stretches of connected discourse on a number of topics pertaining to different times and places; however, understanding is inconsistent due to failure to grasp main ideas and/or details. Thus, while topics do not differ significantly from those of an Advanced level listener, comprehension is less in quantity and poorer in quality.
Speaking : Able to handle successfully most uncomplicated communicative tasks and social situations. Can initiate, sustain, and close a general conversation with a number of strategies appropriate to a range of circumstances and topics, but errors are evident. Limited vocabulary still necessitates hesitation and may bring about slightly unexpected circumlocution. There is emerging evidence of connected discourse, particularly for simple narration and/or description.
If you pass both the interview and the confirmation test, you will have completed the Spanish language requirement and will be eligible to enroll in 200-level courses.
I took French through high school and received a 5 on the AP exam, though am planning to continue taking French classes at Princeton. But I also would like to learn Spanish and Portuguese during my undergraduate career. Do you think that this ambition is plausible?
Your ambition is completely attainable. Learning a third or even a fourth language is always easier than learning a second one. After learning another language, individuals can transfer language-learning strategies they have acquired to subsequent language learning and become better language learners in general. Furthermore, being all the three languages from the same family (i.e. Romance languages), you will greatly benefit from the similarities between them, not only regarding vocabulary, but also (and more interestingly) grammatical patterns.
You should also explore the opportunities offered by international summer language programs.
In short, if you follow the right path and put the necessary effort and dedication, you should leave Princeton University being fairly fluent in all the three languages.