Google's John Mueller has just published 13 tips for moving an http site to https.
These tips include whether it's ok to have the whole site https - that answer is no, it's not necessary.
Moving to https can be done section by section, and need not be done all in one go.
Google is usually good at working out http to https moves, so search drops should not happen, but can happen with bigger sites. The caveat from John, there's no guarantees.
Use the search console to check anomalies.
Crawling will take time, depending upon the site size, and Google moves per url.
You can see the others here.
[
plus.google.com...]