Is that even possible, 802.11b on 5GHz? Might it be some kind of fallback?
Not only does 802.11b operate only in the 2.4GHz band, it also uses DSSS instead of OFDM to communicate. There is no way an device using 802.11b can communicate with a device using a newer standard like 802.11g or 802.11n (assuming 802.11b legacy support is disabled on such a device).
If a newer device were to "fall back" to support 802.11b, it would only operate in 2.4GHz and only use DSSS for the communications. End result is that if your AP is showing it as connected to 5GHz as an 802.11ac device, you phone probably has a cosmetic bug displaying incorrect information.
the phone gets disconnected after ~30 sec after locking the screen
This is typical behavior for many mobile devices. When the screen locks, the device assumes it isn't being actively used and enters into a sleep or power save mode. This often includes shutting off the 802.11 interface or at the very least putting it in power save mode (if the network supports it).
If a mobile device were to continue to act like it was being used even when it wasn't, it would continue to consume power from the battery and significantly decrease the time a device could operate between charges.
I still recieve WhatsApp&Co messages on a (roughly) 30-40 minute basis.
Your device, when locked/sleeping will continue to wake up periodically to check for updates (notifications, alerts, etc). These can either be data that is "pushed" to the device/app or it may be the app "calls home" in a more active manner.
So...to put it crudely: what gives?
My best guess is that everything is behaving as it should, except for a small cosmetic bug where your phone is reporting 802.11b instead of 802.11ac.
2No, 802.11b is 2.4 gig only. – davidgo – 2017-12-12T19:03:10.270