Baby wearing not likely since over time 30-40 years of lugging a child around takes its toll on the back. Also it is very common to have more than one young child in care at a time. Also it is more likely that the caregiver at least to start will have their own young children and would give the sling position to their own first.
On the cloth diapers yes there are some home daycares that will accept them. I take them but the parents are requested to use a liner and if they do I will remove as much fecal matter as I can. Otherwise whatever is in the diaper is bagged (provided by the parent) and put in their carry bag (usually a washable waterproof drawstring or zippered bag). The idea is that I can give the cloth diapers only the treatment I give the disposables. I do not dump, clean out poop as it can cause splashing and contamination of the toilet. Any handling can lead to the spread of disease from child to child and diapering is one of the areas we try our best to contain. Ok this is probably more detailed info that you wanted but it is the rule of many agencies as well in terms of accepting cloth diapers. For a caregiver that says they will dump and rinse you might also want to find out what measures they are taking after to make sure the toilet area is sanitary for the other children since some day it will be your child out of diapers and sitting on the toilet seat and washign their face and hands in the sink.