Unless you're literally looking for someone who can be productive within the first 2 or 3 days of hiring (which means your product/stack is fairly generic and you're hiring some specialist), I don't think this is a great kind of hiring methodology. I recognize you say "we don't have months to get them up to speed", but I think your whole post would be more true if you said "one month" or "2 weeks" rather than "months to get them up to speed".
Personal anecdote/case study:
I interned on the frontend team at Mixpanel in 2011. I had written about 200 lines of Javascript prior to starting work, not a ton of HTML, and literally no CSS. I had however done quite a bit with Python/Django (which they used). My first month consisted of me "getting up to speed" where I was working at a lower rate than others on the team. By the end of summer, I was a fairly productive member of the (3 person) team, building products with tools I had previously had very little experience in.
Fast forward 2+ years:
I've now done 2 years of college. I spent one summer writing distributed machine learning tools for fraud detection, and another summer during deep learning research. The majority of my computer science classes are just theory (no programming), but I've done a bit of programming in C/Python/Rust (for a choose your own language thing) for school and also a bit of programming in Python on the side. Now I apply for your frontend job.
>I'm going to ask them to explain how a closure works
Closes over internal state, talk about read-only (Python)/ read/write (JS) closures and how read/write closures allow you to make basic objects out of functions.
>How they deal with AJAX
Use a callback? Not sure what this question is really asking. Potentially do some kind of client side queuing for some special cases. How to implement server-side push is more interesting.
> What they think about "!important".
Overrides all other CSS rules iirc. Not a best practice thing to use, but still a useful hack to keep in the toolbox.
> Things to be careful about with floats.
I don't remember specifics, but I remember floats can be a bitch. Just Google any problems I'm having. I believe the type of container that floats are in matters.
> How CSS precedence/specificity works.
Could probably work out an example. In general, element inherits all rules that apply to it, and more specific rules overwrite less specific rules. I don't remember the non-trivial ordering for more specific -> less specific (ie id is more specific than class), but would be very easy to look up.
> How to architect a webapp
Would be more comfortable talking about the server-side component, but could talk about client-side code design.
Summary: I'd probably do alright but not exceptionally on your interview. You might give someone else the job. They would probably be more productive on day 1, but I don't know about by the end of week 1.
The twist: If I was interviewing for a frontend job, I'd take a few days to study all of this stuff and significantly increase my interview performance. Would that make me any better at actually doing the job? Probably marginally.