My LW acts in a strange way. At first it downloads
fast (for my connection speed) at 20kb/s even from one host. And on my modem "receive" light is lit nice and steady whereas "send" is flickering.
But then after a half an hour the speed drops to
1-3kb/s even from several hosts, "send" is lit steadily but "recieve"
starts to flicker. At the same time there is no upload to anyone. What the heck is it sending?
After I updated it to 4.2.6 - same thing.
Thank you.

Look in the Monitor page (View Menu-Monitor). You might be sharing chunks of the file you just downloaded. It's called Partial File Sharing and is the reason you can get such great speeds at first: someone else like you is sharing the chunks they've downloaded, and after 1/2 an hour they've run out of chunks too. Just repeat the search and new sources should be found again.

The monitor says 0 active, 0 queued.
I found that when I press "restore defaults" in the preferences (even though I don't reset anything) and restart the LW. everything works fine for another 1/2 -1 hour. and after that it's back to activated "send" and even "recieve" without any obvious download or upload.

Not sure. (You may be running as an UltraPeer, which uses us about 7KB/s upstream).

Check the Tools->Statistics->Bandwidth->Upstream for a breakdown of the bandwidth LW is sending. The http stats are for file transfers; the gnutella messages are for searches and connections.