> I guess UI could kinda work around this to a degree by showing if a given message was delivered yet or not, right ?

It already does.


> What's the main problem with this ? DoS potential (users flooding the network with events/node storage exhaustion ?).

Yes.

> Is it possible to have a server at home receive the message, which server then lights up your mobile when you get back in signal?

Not yet, but it will work like that in the future. All devices will eventually sync the message backlog. So if your server is online to receive message and your phones comes on, the phone will fetch missed messages from the server.