Update: I got it working! It only took fitting OEM Denso O2 sensor...it seems that is is only happy with Denso and nothing else
Now the AC lines going back seem to be leaking due to corrosion
P.S.
It also summarizes my Ebay experience: Chinese knockoff O2 costs 30$...I ordered three different ones and none worked right.
Finally, I bit the bullet and ordered OEM Denso from Ebay Chrysler parts dealer (cost me 90$ here in EU). And he sends me Chinese knockoff again!! When I complained they did the usual "sorry, somebody packed wrong. You can get 15$ refund". After some more mailing they agreed to send OEM for free and bingo, everything works.