How do I distribute CiviSurvey by email, and then analyze the results?
Although you're putting together a survey, the CiviCRM tool you'll want to use is the Profile.  Create a new profile with the custom fields along with any standard ones you want to include.

You'll then want to send an email with an automatically-personalized link to the profile--that way, everyone's responses will go on his or her own contact record without having to log in.  The full directions are here (follow the directions for Profile): https://aghstrategies.com/content/how-create-one-click-personalized-links-civicrm-emails

The analysis capabilities in CiviCRM reports are kind of crude, but you'll be able to export the results into a spreadsheet and do any kind of statistics you need.

A note about "surveys": this use case is collecting information into custom fields on the contact record, so that's a natural use for a profile in "edit" mode.  There is a feature in CiviCampaign called "survey" that is oriented toward collecting information through phone interviews or door-knocking.  You'll have the fields on the contact and/or the activity, and interviewers will fill it in.