I've had a bit of an idea for a while that at the end of the interview when they ask if I have any questions, I would say something like "I like this job, I need this job & I'd be bloody good at this job, what do I need to do to make sure I get it?" but I constantly vary as to whether this is a good straight up enthusiasm thing or borderline begging.
It's not necessary (and sometimes not advisable) to mention things like "I like this job" & "I really want this job". The fact that you want the job is obvious - you're applying for it. Rule #1 of job applications is: never apply for a job you don't want. It'll shine through.
Keep questions objective, informed and to the point. Try to show through the questions that you have the required insight into whatever knowledge the job requires.
You should also think about what you would answer if they ask "Why should we hire you". If they don't ask it, try and get some of the key point of why they should hire you through during the questions and/or smalltalk. If you can't think of any reason they would hire you, don't apply for the job.
When I applied for part-time jobs as a student the interviews where never that rigorous though. Most of them were 30-45 minute talks with maybe a little quiz and brainteaser thrown in. But when I interviewed for proper engineering jobs ... phew.
Why would you send a letter? Thank him/her/them there and then. To follow up on your application post-interview, well you presumably have a phone. Use it.