It's mixed: that CSS file is only cached until the next time you change it and browsers, especially mobile ones, do not have enormous caches. As with most engineering problems the best solution is a balance: put enough CSS in the page for the document to render and either prefetch or demand-load resources which aren't as important, all the while working to keep the absolute size down so your worst-case performance is reasonable.

As an example, if you had something like an item page and a detailed viewer which the user could choose to open, the item page's HTML could have its critical CSS inline and a <link rel=prefetch> tag to tell the browser to preload the viewer's CSS so it will likely be in the cache by the time the user opens the viewer.

If you visit several pages on a single website, then yes. But if you want to scroll through AMP pages from different websites in the search results, caching doesn't help much.

If I'm pulling the page over an encrypted connection, is there any opportunity for caching?

Yes: your device can always cache it, if you use a trusted proxy (think enterprise networks) it can be cached, and if the site uses a CDN it can be cached there as well.