Sourdough starter and long term feeding
A well-established starter will be fine in the refrigerator, even (in my experience) if you go well beyond weekly feedings. You could also freeze it, though I have not done that myself. No matter what my feeding schedule, or length of storage, I usually plan for a few days of counter-top feeding and revival before baking, just to ensure peak activity.  I've used all sorts of flour combinations.  For the home baker, it makes little difference, so yes...you can use all rye or a combination of rye and wheat.