What do you mean by "new"? If you just want to know the number of nodes, the node ids are assigned sequentially.
Number of new opening nodes
Again, I don't know what "new" means, so I guess you mean all nodes. You can't easily query this statistics, but I think there's no harm in telling you the counts of root nodes for some sections. (A few sections are omitted on purpose.) The following numbers are current as of this post, will not be updated later, and include unapproved and even reaped nodes.
This one is easy, you can query the list of all of them on Anonymous Monk's writeups: the count listed is often inaccurate, but you can figure out the exact count by changing the "starting at" field.
Number of messages in the Chatterbox, number of people who commented in the chatterbox
As mentioned by others, you can get the numbers for a one-week window from mojotoad's cbstats or from Tanktalus' cbstats. If you just want to know the numbers from the start of time, the number of messages might be related to the message ids you can see in the Tickers, but I've no idea if these started from 1, I think they might have been reset once, and I think they include private messages and possibly other things too. As for the number of monks who ever talked in the chatterbox, the gods may be able to extract an approximation for this number by looking at how many users have a last_chatter setting. This setting stores the last line you talked in the chatterbox, so that the site can filter accidental double submits.