(1) IMAP and POP3 (and EWS, Exchange) are different ways for the app to connect to your mail server. The sync / cache logic is (mostly) independent of that.
(2) "cache" in "messages to cache" is an AquaMail term (and a universal "computer" term), does not necessarily relate to "cache" as "the Android cache partition or the Android term in system settings app -> apps".
In fact, AquaMail stores the text of all messages that have been loaded onto the device in "internal memory".
Attachments are cached on the "large built-in memory" (Android calls this "external memory", used to be the microSd in 2.* days, not anymore). This is your "16 GB" / "32 GB" partition.
Since 1.6.2, it's possible to "cache" attachments on the "real" microSd (not the "built-in 16 GB" partition), please see app settings -> look and feel.
(3) Attachments or messages are not backed up by the app's "backup and restore" -- it is assumed that actual messages can always be found on the mail server
(4) You do not want your on-phone storage to build up too much.
Android devices are "not quite" Windows PC's in terms of storage capacity and/or disk performance and/or RAM.
How many messages the app "stores" on the device is the "messages to cache" setting. Please be reasonable and don't dial it to "5000" all at once -- it will affect how much memory the app will use and will affect performance too if too large.
Now how many of those messages are always "fresh" (up to date with the mail server in terms of read/unread and their existence) is the "messages to sync" and there is a setting for that too.
I would recommend "messages to sync" at 100 and "messages to cache" at 250, maybe 250 and 500.
If you're going to use IMAP push mail, 100 / 250 is better than 250 / 500, or else it might generate too much network traffic.
(5) In an Exchange account, the app can access your server side Calendar and sync it with Android's Calendar storage (and then you can use Google Calendar, S Planner, or any other calendar type app to view / make changes / create invites).
IMAP or POP3 do not provide access to server side Calendar (even if there is one in your web mail or in your Outlook on Windows).
Therefore:
For those account types, the app is capable of displaying the content of "calendar invites" (.ics files) in your messages, you can tap one to see its details, and then you can "accept / decline" and then:
- the app will send a response to meeting's organizer / invite sender
- will record the event in one of your phone's Calendars, there is a drop-down list if you scroll down AquaMail's "calendar event view" popup
By default, pretty much every Android phone has a Gmail account and there is a Calendar under that account.
If you choose that one, then AquaMail will save the event there.
Unfortunately, the list of attendees is not saved -- because of a Google issue, saving the attendees will make Google send *invites* from the just saved event, ignoring the fact that the organizer is not you, but rather someone else, and you're just one of the attendees.