(1) What is a ChatMail account/identity actually? I understand that ChatMail technically relys on classical e-mail infrastructure.
yes. chatmail relies on classic email infrastructure, currently postfix and dovecot, with a few tweaks that makes chatmail perfect for messaging and incredible cheap and easy to run:
- chatmail allow instant onboarding
- chatmail allows encrypted messages only, resulting in peer-to-peer end-to-end-encryption - also this is a barrier for misusing the relay - you need the public key of the recipient
- chatmail allow instant delivery by supporting PUSH notification, esp. on iOS there is no alternative to that
But users don’t seem to require a classical e-mail account.
yes.
best is if average user do not even think about if they need an email account or not.
install the app - choose a name, done.
this is only a thing for long-term Delta Chat users, as it was different before 
(2) Can I keep/move a ChatMail account to another host?
great question!
in fact, we’re regarding that “right to exit” for chatmail operators as a very basic thing, where other decentralized services are failing or put a lot of burden to the operators, see xmpp or mastodon as examples.
in the past, it was already experimentally possible to change the provider. we’re currently aiming to get that out of experimental. the next releases will no longer identify the user primarily by and address, but by the cryptographic identifier - this will make it much easier to change transport chatmail relays - or even use multiple. stay tuned
(user not using chatmail, still can use addresses as anchors, but that is not the way most users will experience Delta Chat, as said, most do not even know about that it is about email)
this also answers (3) - yes there are minor differences in relay, but as it will be easy to switch, they do not matter much, much less as eg. on mastodon. all chatmail relays and even classic providers are compatible.
I hope messages (successfully received) be kept on the device, correct?
yes
Secondly: If receivers are offline, e.g. in holidays for 20+1 days, will they miss some messages?
if you do not switch on your device in that three weeks, yes, you will miss messages when using chatmail. note, however, this is not a limitation of Delta Chat, but a consideration of many chatmail operators, that way, eg. they do not need to worry about GDPR, as this is within required timespans. the default makes chatmail relays easy to secure to operate without getting in conflict with laws, which is an important consideration as well, and results in the many chatmail servers we already have today.
still, you are free to use relays or classic providers with larger timespans.
(5) Compatibility with non-DeltaChat e-mail users: When using a ChatMail profile, can I still exchange messages with non-DeltaChat users over their e-mail address?
not easily, as chatmail enforces encryption, that is handled gracefully by chatmail/core, but not by lots of other “big tech” or classic tools. Proton Mail, otoh, should work.
(6) Compatibility between classical DeltaChat and ChatMail users: Can they communicate?
yes, as chatmail is mostly a subset of classic email, communication works. still, configuring classic email in Delta Chat may be a pain point, esp. for “big tech”, and lacks some of the advantages mentioned above