There certainly are some advantages of iTerm2 but the ones you stated are very easily done in Terminal.app:
1. Settings > Profiles > Shell > When the shell exits: [Close the window|Close if the shell exited early|Don’t close the window]
2. macOS standard for all applications is the following.
- next tab: ⌃⇥ or ⌘⇧]
- previous tab: ⌃⇧⇥ or ⌘⇧[
If you really want to change that, you can do so in System Preferences
3. Settings > New window with profile: Pro