Hi there,
thank you for the help.
(odd enough i posted an hour ago, but somehow this is not visible to me anymore ... whatever)

1) The router is an ADSL-router modem D-LINK DSL-G664T. I just installed the most current firmware version, number: "V3.00B01T02.EU.20060213".
After getting it up and running, the behavior however, remains the same
Here is what ethereal said:
Src Dst Protocol Info
192.168.1.2 192.168.1.1 DNS Standard Query AAAA web.de
192.168.1.1 192.168.1.2 DNS Standard Query Response
192.168.1.2 192.168.1.1 DNS Standard Query AAAA web.de
192.168.1.1 192.168.1.2 DNS Standard Query Response[Malformed Packet]
192.168.1.2 192.168.1.1 DNS Standard Query A web.de
192.168.1.1 192.168.1.2 DNS Standard Query Response A 1.0.0.0
192.168.1.2 1.0.0.0 TCP 54214 > www [SYN] .... etc pp

If Konqueror makes the request, it looks like this:
192.168.1.2 192.168.1.1 DNS Standard Query A web.de
192.168.1.1 192.168.1.2 DNS Standard Query Response A 217.72.195.42
192.168.1.2 192.168.1.1 DNS Standard Query AAAA web.de
192.168.1.1 192.168.1.2 DNS Standard Query Response[Malformed Packet]
192.168.1.2 217.72.195.42 TCP 45640 > www [SYN] .... etc pp
217.72.195.42 192.168.1.2 TCP www > 45640 [SYN, ACK] ... etc pp
which obviously is the way to go ...
*shrugs*

2) Here is the ifconfig -a output:
th0 Protokoll:Ethernet Hardware Adresse 00:118:5E:AA:C5
inet Adresse:192.168.1.2 Bcast:192.168.1.255 Maske:255.255.255.0
inet6 Adresse: fe80::211:d8ff:fe5e:aac5/64 Gültigkeitsbereich:Verbindung
UP BROADCAST RUNNING MULTICAST MTU:1500 Metric:1
RX packets:2302 errors:0 dropped:0 overruns:0 frame:0
TX packets:2527 errors:0 dropped:0 overruns:0 carrier:0
Kollisionen:0 Sendewarteschlangenlänge:1000
RX bytes:1282796 (1.2 MiB) TX bytes:481236 (469.9 KiB)
Interrupt:17 Basisadresse:0x2000

eth1 Protokoll:UNSPEC Hardware Adresse 00-11-D8-00-00-04-CB-92-00-00-00-00-00-00-00-00
BROADCAST MULTICAST MTU:1500 Metric:1
RX packets:0 errors:0 dropped:0 overruns:0 frame:0
TX packets:0 errors:4 dropped:4 overruns:0 carrier:0
Kollisionen:0 Sendewarteschlangenlänge:1000
RX bytes:0 (0.0 b) TX bytes:0 (0.0 b)

eth2 Protokoll:Ethernet Hardware Adresse 00:118:5E:9A:8B
BROADCAST MULTICAST MTU:1500 Metric:1
RX packets:0 errors:0 dropped:0 overruns:0 frame:0
TX packets:0 errors:0 dropped:0 overruns:0 carrier:0
Kollisionen:0 Sendewarteschlangenlänge:1000
RX bytes:0 (0.0 b) TX bytes:0 (0.0 b)
Interrupt:19 Speicher:ec000000-0

lo Protokoll:Lokale Schleife
inet Adresse:127.0.0.1 Maske:255.0.0.0
inet6 Adresse: ::1/128 Gültigkeitsbereich:Maschine
UP LOOPBACK RUNNING MTU:16436 Metric:1
RX packets:14 errors:0 dropped:0 overruns:0 frame:0
TX packets:14 errors:0 dropped:0 overruns:0 carrier:0
Kollisionen:0 Sendewarteschlangenlänge:0
RX bytes:700 (700.0 b) TX bytes:700 (700.0 b)

sit0 Protokoll:IPv6-nach-IPv4
NOARP MTU:1480 Metric:1
RX packets:0 errors:0 dropped:0 overruns:0 frame:0
TX packets:0 errors:0 dropped:0 overruns:0 carrier:0
Kollisionen:0 Sendewarteschlangenlänge:0
RX bytes:0 (0.0 b) TX bytes:0 (0.0 b)

So ... i hope, although there are some german terms in between, that it is comprehendable (well, the format is always the same, isn't it?)

I am currently quite lost, and i really appreciate any help or hint anyone could give on that matter.
I must admit, that i am not THAT familiar with Linux, although i have been working on Linux machines for some years now ...
If there is any more information needed, please let me know.

Best regards and thanks in advance
Christian