that is the last week of the season and half term for us folks in the UK so it will still be a busy week - yes the odd restaurant might close up - but Kas is a working turkish town as well as a holiday resort and therefore there will be plenty enough open for you - don't worry there!
As regards weather - be prepared for everything - you may get blazing blue skies and sunshine and warm - but you may get torrential rain and thunderstorms. We go to Kalkan every year for this week and have always been very lucky with the weather - but you do take pot luck at this time of year! If sunny - it will be great to sunbathe and swim in the sea which will be like a bath. It may be a bit chillier at night!
Fly into Dalaman or Antalya - probably Dalaman will have the slightly quicker transfer time - just under 3 hours as opposed to Antalya which will be about 3.5 hours. You can then arrange a transfer or take the bus from either airport!