Can an entire data frame be used as a prediction variable?
First question; is it possible to pass an entire data frame as a variable to a model?


No, each feature must be a single value. In other words you could provide the data frame as a vector containing all the values, assuming the size is fixed: each column would correspond to a specific cell in the original data frame.

But I think an even better option in your case is to look into methods which take (chronological) sequences into account. Conditional Random Fields might be a good option, assuming you need to predict the target variables for the whole sequence?