1. That seems workable. I don't know all the details about the nostr protocol, but AFAIK follower lists are public, so stashing your follower list on your own server should allow the server to start checking those relays
2. Having a lot of connections on a mobile device isn't great, but with the above approach, you'd only need endpoints to connect to your own server (and some public relays to assist in finding new people to follow). Servers can handle thousands of concurrent connections, and there's no reason the connections have to remain constantly open to every relay.
I'd want to make sure that each of my clients has a complete copy of everything I'd need to spin up a new server. This would be things like DMs, following list, follower list, relay list, and so forth. I think that was assumed here, but I just wanted to point out that it's an important feature. Little servers go away all the time, so we want to make sure users have the confidence that people can recover when that happens.
Encryption can satisfy the desire for confidentiality, but it's important to be clear about what is being stored where and who has access. For example, "DMs are stored on your server, but the server can only see the sender and recipient, not the contents", and "list of people you follow is on your server and the server can see everyone on this list"