We can use the Data Explorer to see how often we up- and downvote. This query compares the number of posts (including deleted ones) and the number of up- and downvotes for all sites in the network. On MathOverflow, a post receives (on average) 5.29 upvotes and 0.46 downvotes.
Of the 176 sites in the network, we're #23 when it comes to upvotes per post, and #...
I can answer this part of the question with the Stack Exchange Data Explorer.
What is the maximum degree of a node in $G$? How are the degrees of nodes distributed?
This query shows a list of questions with the most links.
Number of links
Proposals for polymath projects
Examples of common false beliefs in mathematics
Not especially ...
Here are some additional SEDE queries. (As my knowledge of SQL is rather limited, take all of this with a grain of salt.)
Percentage of Upvotes and Percentage of Upvotes (multisite). MathOverflow currently gives 91.94%.
We can obtain average number of up/down-votes on post which weren't deleted if we look into table Posts rather than PostsWithDeleted. (But ...