Hey @Deleted,
1. Your users will likely get prompted once or their username and password. Assuming you were running AADC they should just enter it in once and be good.
It is worth noting the one thing you can count on is that you cant count on outlook. I have done hybrid moves probably 3-4 dozen times for clients of all sizes, and everyone you are going to have some users who just work right away with no prompt, most users who get prompted, and some users that no matter what you do to the old profile wont work and you have to rebuild it. Just expect that to a small degree. MOST of your users should get a username/password prompt, do it once, and be good to go.
2. Expect any permissions to automap down over the next few hours. Depending on which version of exchange you are coming from this may or may not be happening, but in O365 all permissions are by default automapping in. So users will start to see other mailboxes show up they have access too, etc.
3. Cache mode is entirely up to you based on your network capacity and security/compliance settings. I normally did at least a year if the client had a decent connection, but in some cases we made it much smaller or larger (IE everything) based on what they needed. Honestly this one is mostly personal preference, but i would say whatever your settings are now would be fine for the move.
4. The MSI office works perfectly fine for running outlook for O365. It will just not have ALL the new bells and whistles and will not be tied to the O365 subscription, such as focused inbox etc. Assuming you got licenses that have a version of Office, you will want to eventually upgrade the office suite on you computers, but that can, and often is, done post migration, as to not change to many things at once. (again this one comes down to personal preference, some of my clients saw it as a band-aid to rip and do everything at once).
5. If you are running Azure AD, there is a great chance your devices are hybrid AD joined, as any local domain joined machine is going to be in, but this wont matter for your migration unless you are trying to fully go azure ad, and getting rid of your local AD system.
* You asked allot of good, deep technical questions that shows you have done your research. The fact of the matter is most of this stuff is way beyond what actually comes into play in a basic hybrid move, so you are probably over thinking it! As long as your AD is in a good place, you are running AADC, and have setup the hybrid config, using the HCW, you are going to be fine!
Hope this helps, let me know if you have any more questions.
Adam
