[1] Signal is working to support an encrypted "cloud backup feature" (some hints on this are on their code base), as per "sync" that's already done in the forward direction by Signal (by sending all new messages to all your devices) I'm sure you could provide some sort of backward sync as well. [3] Signal already supports groups up to 1000 people iirc, I'm sure a read-only channel larger than that could also be doable. [4] I'm not sure why that would not be possible.
I'm not sure exactly what [2] refers too but nevertheless I have some doubts that would cause a blocker.
I used Signal as an example since it's a well known encrypted messenger; although I must acknowledge it's not really a Telegram competitor and vice versa (one is a secure messenger and the other is a social media app).
That said, (proper) E2E encryption makes everything harder to do - again, you can take Signal as example and their development speed. But, I'd argue, is not impossible