Hello,
You can do both of these customizations. To setup notifications per-account, the path is Settings > Manage accounts > Your e-mail > Special Settings > Message notifications > Enable them, then tap Manage. You'll be taken to the relevant notification category in your Android Settings where the sound can be adjusted (it depends on the device vendor if the sound option is available per category, but I think Google have it).
To setup notifications for specific senders, the option is in Settins > Priority notifications > Enable them, and again tap Manage to visit the notification category in Android Settings.
Your notification sound likely hasn't transferred on the new device so you'll have to dig up the file if it is custom.
Hope this helps!
Martin
