on-topic/off-topic has already been quite extensively discussed. Even though there is still some ongoing debate about "target audience" or whether "JLU should accept cultural questions", I think most people agree with the original beta statement of purpose ("everybody welcome" and "only somewhat-language-related questions"). The rest is just fine-tuning.
Current FAQ looks good. There's been a few questions pertaining to possible FAQ modifications. I will now go over them and make sure they are all tagged appropriately and we can quickly go over in one fell swoop at the end (Update: done).
Question format has also been extensively discussed when the site was in pre-launch. Not sure we need any more examples, but...
Tagline: Not sure what else beside our current title and a one-line welcome message is needed. Based on other SE sites, something like "Welcome to Q&A for students, speakers and anybody with an interest in the Japanese Language" could do. The "students, speakers etc." part is the only unknown and depends a lot on the outcome of our "target audience" debate.
Promotion: Like any other SE site, and like most things in general, 99% of promotion will be word-of-mouth through social networks and the internet. Beside encouraging people to do so, not sure what else there is (providing options and tools to do so, is definitely SE's job, not ours). Perhaps later on, we can organise to pick particularly good question/answers and spread them around ("Share-your-favourite-question Friday" or something), but that doesn't strike me as a priority.
Look and Feel
Will be a hard one, I feel. From experience, everybody has an opinion on how things should look, not two people alike. Also: everybody is a critic, but few really want to spend the time it takes to make a logo/design etc.
How about starting with the Logo, with a question dedicated to people posting their ideas (as in: actual graphics) and other people suggesting improvements/changes. Once we've narrowed it down a little (and assuming we even have the luxury of choice), we can organise a vote of sorts to pick the logo. Update: over here!
Once a logo is picked, it is rather easy to pick the rest (matching colour theme etc).