Edit: Finally I found the problem:
After rechecking the configuration I eventually tested it with another USB Wifi adapter. And I was really surprised to see that everything was working then. ARP requests were being received and answered by the clients. Ping and ssh between arbitrary clients was working, too.
Just to be certain, I changed back to the first USB Wifi adapter. And again ARP requests were not received (and answered) by the clients. Thus I can confirm that it was not an issue with configuration of hostapd or with kernel arp tables. The problem was the driver for the Wifi adapter.
Here are the details:
ID 0bda:8812 Realtek Semiconductor Corp. RTL8812AU 802.11a/b/g/n/ac 2T2R DB WLAN Adapter
- Not working correctly.
- ARP requests are received by the access point, but they are not received by the clients.
ID 0bda:b812 Realtek Semiconductor Corp.
- Working satisfactorily.
- ARP requests and ARP replies between arbitrary clients are working correctly.