So I did try the procedure from scratch.
This time not just copy/paste but also looking at the steps and thinking, what is the aim and thus adjusting few commands. Particularly I was messing with the step #6 - the "mv" and revised "cp" commands.
With the mv I have renamed the rt2860sta.ko into rt2860sta.ko.dist which resided in my .../net/wireless
Looking at the revised cp and my directory structure, I first created a directory called "rt2860" in my .../staging/ and then copied the rt2860sta.ko into that newly created directory.
The "..." is /lib/modules/3.2.0-35-generic/kernel/drivers/ and yes, the 3.2.0-35-generic is what uname -r returns.
Result: still the same situation - wifi not working, although connected.
For better orientation, I will now post output of several commands, maybe you can spot something.
dmesg | grep -e -ra0 -e rt2
[ 20.714703] rt2800pci 0000:01:00.0: PCI INT A -> GSI 19 (level, low) -> IRQ 19
[ 20.714730] rt2800pci 0000:01:00.0: setting latency timer to 64
[ 20.789605] Registered led device: rt2800pci-phy0::radio
[ 20.789963] Registered led device: rt2800pci-phy0::assoc
[ 20.790187] Registered led device: rt2800pci-phy0::quality
lsmod | grep rt2
rt2800pci 18340 0
rt2800lib 53298 1 rt2800pci
crc_ccitt 12627 1 rt2800lib
rt2x00pci 14202 1 rt2800pci
rt2x00lib 48875 3 rt2800pci,rt2800lib,rt2x00pci
mac80211 436493 3 rt2800lib,rt2x00pci,rt2x00lib
cfg80211 178877 2 rt2x00lib,mac80211
eeprom_93cx6 12687 1 rt2800pci
What is this Invalid misc:10 ? Does it lead to anything?
lo no wireless extensions.
wlan0 IEEE 802.11bgn ESSID:"MI6_guest"
Mode:Managed Frequency:2.412 GHz Access Point: CC:5D:4E:B4:05:C9
Bit Rate=72.2 Mb/s Tx-Power=20 dBm
Retry long limit:7 RTS thr:off Fragment thr:off
Link Quality=54/70 Signal level=-56 dBm
Rx invalid nwid:0 Rx invalid crypt:0 Rx invalid frag:0
Tx excessive retries:0 Invalid misc:10 Missed beacon:0
eth0 no wireless extensions.
ERROR: modinfo: could not open /lib/modules/3.2.0-35-generic/kernel/drivers/net/wireless/rt2860sta.ko: No such file or directory
I understand the last 2 errors, as I have renamed the module to have ".dist" at the end.
FATAL: Could not read '/lib/modules/3.2.0-35-generic/kernel/drivers/net/wireless/rt2860sta.ko': No such file or directory
What I do not understand is, how come the wifi gets connected, even when the module cannot be loaded?!
Well, any help is still greatly appreciated.