I cannot Speak to all your questions. However, I Think that the K10 and the kit Is a good starting point. But To Buy Both the DA50-200 and the Sigma 70-300DG is a bit over kill. You basically have Two Lenses that Cover the Same range.
While its your choice, I would take one or the other.
As to the Sigma Being a good lense With the teleconverter. Just Keep In mind that you add the teleconverter and you add between 1.5 and two stops to the Lense. So for pictures to Be great, you will need a very Bright day. Not saying it cannot Be Done, just be aware.
Having said all the above I love my Sigma 70-300 APO DG Macro and would highly reccommend it.
Just my two cents