Montastic uses many servers located in the US to check your URLs. They change on a regular basis this is why we cannot give a fixed list of IPs.
No. Montastic checkers will probe your servers from different locations on the Internet. Your server needs to be accessible to Montastic checkers.
Montastic will try to fetch a URL for 45 secs twice. If both times the URL is unreachable the status changes to unreachable and recipients are notified of the new status.
Montastic uses a combition of HTTP HEAD and GET depending on what is most efficient and appropriate for that particular URL.