1. The text field is actually a filterable "select"-type field, not a raw search. It should show you completions that you should click; if you're not seeing any, you might be encountering some JavaScript error somewhere. It does look like keyboard-only navigation is broken/unsupported, though, which seems important to add -- I'm forced to use my mouse to click the option I want.

2. The homepage requires you to choose an artifact/package first. Click "java.base" and then you can find SimpleDateFormat with the "search" field on the subsequent page.