> First question. When I open the TVHadmin-JS web Interface there is no possibility to set user and password. Nevertheless TVHadmin-JS web Interface shows me the EPG and timer. It seems to work.
If you have login credentials for the Tvheadend UI saved in your browser (cookies), TVHadmin-JS will use those.
> I have set in TVHadmin-JS the timer clash and single tuner. Then I set one timer and the timer got a green tick. Then I set a second timer and a third timer. All three timers on the same transponder. Every timer now had a yellow tick. Then I set a forth timer on another transponder. Though I have a dual tuner all four timer now had red ticks.
That is correct. TVHadmin puts a red mark against all of the timers which are involved in the clash, so you can decide which timer(s) to move or cancel.
> Then I set "timer clash and multi tuner" but still the same. My understanding is that TVHadmin should have now four yellow ticks or one green tick and three yellow ticks. Why that doesn't work?
TVHadmin may not be correctly recognising your dual card as two tuners. Can you see both tuners on the TVHadmin 'status' page?
> It's my understanding that TVHadmin-JS only reads data from TVHeadend. TVHadmin-JS doesn't wright data back to TVheadend. So my next question is. I have TVHeadend as backend and 2 Kodi clients as frontend. Is it possible that the Kodi clients get informations from TVHadmin that timers have a green or yellow or red tick? I don't think so! But that is what I want to have.
TVHadmin steps through the timers list in time order, and allocates a tuner to each timer using (hopefully) the same algorithm as Tvheadend will use. To see the information in Kodi would need something similar added to either Tvheadend or the Kodi plugin.