Your suggestions are really good but do you know that if messaging privately is allowed people will be disturbing others with higher Steem power for votes...thereby increasing spamming rate. I don't think that's a good idea.

Then for notifications Hive account@ginabot has a solution for that already. Just check out the blog and see for yourself.

Then for the new tab I really did not understand what you were trying to suggest maybe you can explain better.

Anyways thanks for this suggestions and keep steeming