Yes, your solution like it is in the picture is possible. Just make sure you enable the terminator resistor on both ends on the red and on the purple line (4 in total).
Late to the chase but it never hurts to have a second opinion. Yes, that will work. I usually position the repeater for best isolation, for example to separate field devices from panel devices. If it makes a Y, then so be it.
No, the standard repeater is a passive device. Siemens makes a diagnostic repeater that is present in the hardware configuration but with a standard repeater there is nothing to do.
Consult the repeater manual for info on it's dip switches. I believe Jobbe is correct about four end terminations - one on the repeater itself using its dip switch.
Concerne the end terminations, I`m not following. Does this mean that the end termination should be "On" at the reapeter split for the encoder(4) and the ET200S(6), and at the last encoder(5) and the last ET200S(8) ?