Multicolumn statistics on large table yielding poor estimations
With a table that large I would consider partitioning.  Unfortunately I can't answer your specific questions (1-3) but in general one of the benefits of using partitioned views (instead of native partitioning) is that the individual tables within the partitioned view are considered separate objects and have their own statistics each with 200 steps.  Here is a post where Kimberly Tripp of SQLSkills recommends for large tables that you consider not only partitioning or partitioned views but combining the two.

In case you don't know a partitioned view is one where you have multiple tables each holding a portion of the data and a view on top with UNION ALLs to combine the tables together.

Here is another of Kimberly's blogs on statistics in case you are interested.  It should help you answer some of your other questions.

Here's an article of Connor Cunningham regarding statistics: Statistics, Damned Lies, and Statistics – What is Statman?