I am looking for some ideas how to arrange a trekking in Phou Kway (or Phou Khao Khouay. )
Have you done a trip there, would you advise on how to arrange it?
I have looked at a web site that offered one day trip for "only"$145 pp
You should be able to do this independently, $145 is a crazy price to pay! You can either hire a minivan to take you there from Vientiane (expensive option) or take a song taew (pick-up truck, local transport, very cheap) from the southern bus station to Thabok, and from there you can arrange for further transport to Ban Hatkai where you can arrange for a local guide to bring you into the national park. Here is a link for more detailed info: http://www.trekkingcentrallaos.com/html/possibletrips_banhatkhai.htm
There is a phone number listed on travelfish for Ban Hatkhai but it's possible that it is out of date: (020) 224 0303. Here is the link to the section on PKK on travelfish: https://www.travelfish.org/location/laos/vientiane_and_surrounds/vientiane/phou_khao_khouay_national_park
It's great that you are going to Phou Khao Khouay, it's a beautiful place to visit but almost no foreign tourists go there! There are numerous waterfalls and rivers to explore by boat and jungle by foot, and the people who live there are some of the friendliest I've ever met and definitely need more business!
Feel free to contact me if you would like me to put you in touch with someone from the village directly, and I'll see what I can do!