I would be curious as too which variety of Linux (other than ubuntu - too many threads out there on exactly my issue) anyone here is using that has no problem with local DNS queries in networks that contain windows, linux and random home network appliances (i.e. nslookup) . I can move on from ubuntu.
I have a really old laptop on the shelf running really old Ubuntu (16.04). Dusted it off and fired up, and reverse lookup works fine on it. So maybe something introduced since that version, but I suspect more likely something is corrupted or messed up on your router.
The default was using localhost for lookups (which was obviously then forwarding the request to the Asus since nothing else knows these hosts) but I then pointed it directly to the router and it worked the same.
For god's sake don't google the specs on the Satellite 1905. A friend dropped it off years ago to recover data off a dead HD, and I figured I had a spare HD, why not throw Ubuntu on it. And it's pretty much sat ever since. Amazingly the SOB still has a good battery, I didn't even realize the adapter wasn't plugged in and hasn't been for a long time.
Anyway, see below, some items redacted to protect the innocent. I get the same results with windows (well, with the obvious differences in how it displays the results).
Dynamically assigned DHCP (no reservation):
username@Satellite1905:~$ nslookup e5470 10.0.0.1
Server: 10.0.0.1
Address: 10.0.0.1#53
Name: e5470.intra.mydomain.net
Address: 10.0.0.117
username@Satellite1905:~$ nslookup 10.0.0.117 10.0.0.1
Server: 10.0.0.1
Address: 10.0.0.1#53
117.0.0.10.in-addr.arpa name = E5470.intra.mydomain.net.
Reserved DHCP assignment:
username@Satellite1905:~$ nslookup ap-front 10.0.0.1
Server: 10.0.0.1
Address: 10.0.0.1#53
Name: ap-front.intra.mydomain.net
Address: 10.0.0.2
username@Satellite1905:~$ nslookup 10.0.0.2 10.0.0.1
Server: 10.0.0.1
Address: 10.0.0.1#53
2.0.0.10.in-addr.arpa name = AP-Front.intra.mydomain.net.
Router itself:
username@Satellite1905:~$ nslookup 10.0.0.1 10.0.0.1
Server: 10.0.0.1
Address: 10.0.0.1#53
1.0.0.10.in-addr.arpa name = router.intra.mydomain.net.
Example using localhost dns but forwarding the queries to the router:
username@Satellite1905:~$ nslookup e5470
Server: 127.0.1.1
Address: 127.0.1.1#53
Name: e5470.intra.mydomain.net
Address: 10.0.0.117
username@Satellite1905:~$ nslookup 10.0.0.117
Server: 127.0.1.1
Address: 127.0.1.1#53
117.0.0.10.in-addr.arpa name = E5470.intra.mydomain.net.