Mathematics behind dynamic logistic growth model

Hi, I have been reading the paper and diving into the source code to would like to ask a couple of questions on a dynamic logistic growth model (where the capacity is changing).

1. The calculation for the initial growth rate of the model seems to be based on the first and last data points, with respect to each of their capacities. Given a situation where the data is increasing, but the capacity increases at a much higher rate, would the initial logistic growth rate be negative? If it is negative, wouldn't this mean that the trend will decrease when the ceiling plateaus?
2. I would also like to ask how does the capacity affect automatic changepoint detection. For example, if the capacity is too low and some data points are above the capacity, will that impact the number of significant changepoints, and how will it be affected?

Thank you!