Those are some pretty broad numbers you're looking for. I'm not sure how valuable the answers could be, but here's some info that might point you in the right direction.
Single Word Vs. Phrase Searching
If you look at just the most popular searches, (top 500) you'll find that it runs around 50% single words. However, the top searches actually make up only a very small percentage of the total number of searches being done. If you look at any particular industry or niche, you'll usually find that only a very small percentage of searches are done with a single word.
A good example would be a topic like golf. The most searched on term within that niche will always be the word golf, but the remaining Top 9 combined will make up the majority of total searches done.
Total Number of Daily Searches
This is a stat that isn't real easy to figure out, because you have to use data from several different sources. Several of the top search engines publicly state an estimated number of searches that they serve in a given time period. There are other services like Media Metrix, or WebSnapshot, that publish market share numbers. If you combine the two, you can come up with a rough number that falls somewhere around 250,000,000 per day.
Now keep in mind that those numbers will only include the major search properties, and the calculations are based in large part on numbers provided from the search engines themselves.