To count threads instead of individual messages, you can add the term "is_root:true" to your search query, for example:
/search/messages/count?q=date%3A%5B1341341612%20TO%201341946412%5D%20AND%20is_root%3Atrue&collapse_discussion=false
This will give you only root messages of threads, which is equal to the number of threads from that period of time.
To get the number of views for a forum for a certain period, I'd suggest using the "metrics" method for a board. There are a few different views metrics, so I'd suggest reviewing the metrics in the admin to get the name of the exact metric you're interested in. The call would look something like (assuming you wanted message views):
/boards/id/YOUR BOARD ID/metrics/name/message_views
This call also accepts a date_start and a date_end parameter to specify the date range.